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# Documents  05C05 | enregistrements trouvés : 65

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## Self-interacting walks and uniform spanning forests Peres, Yuval | CIRM H

Post-edited

Research talks;Combinatorics;Mathematical Physics;Probability and Statistics

In the first half of the talk, I will survey results and open problems on transience of self-interacting martingales. In particular, I will describe joint works with S. Popov, P. Sousi, R. Eldan and F. Nazarov on the tradeoff between the ambient dimension and the number of different step distributions needed to obtain a recurrent process. In the second, unrelated, half of the talk, I will present joint work with Tom Hutchcroft, showing that the component structure of the uniform spanning forest in $\mathbb{Z}^d$ changes every dimension for $d > 8$. This sharpens an earlier result of Benjamini, Kesten, Schramm and the speaker (Annals Math 2004), where we established a phase transition every four dimensions. The proofs are based on a the connection to loop-erased random walks. In the first half of the talk, I will survey results and open problems on transience of self-interacting martingales. In particular, I will describe joint works with S. Popov, P. Sousi, R. Eldan and F. Nazarov on the tradeoff between the ambient dimension and the number of different step distributions needed to obtain a recurrent process. In the second, unrelated, half of the talk, I will present joint work with Tom Hutchcroft, showing that the ...

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## Distributive Aronszajn trees Rinot, Assaf | CIRM H

Post-edited

Research talks;Logic and Foundations

It is well-known that the statement "all $\aleph_1$-Aronszajn trees are special'' is consistent with ZFC (Baumgartner, Malitz, and Reinhardt), and even with ZFC+GCH (Jensen). In contrast, Ben-David and Shelah proved that, assuming GCH, for every singular cardinal $\lambda$: if there exists a $\lambda^+$-Aronszajn tree, then there exists a non-special one. Furthermore:
Theorem (Ben-David and Shelah, 1986) Assume GCH and that $\lambda$ is singular cardinal. If there exists a special $\lambda^+$-Aronszajn tree, then there exists a $\lambda$-distributive $\lambda^+$-Aronszajn tree.
This suggests that following stronger statement:
Conjecture. Assume GCH and that $\lambda$ is singular cardinal.
If there exists a $\lambda^+$-Aronszajn tree,
then there exists a $\lambda$-distributive $\lambda^+$-Aronszajn tree.

The assumption that there exists a $\lambda^+$-Aronszajn tree is a very mild square-like hypothesis (that is, $\square(\lambda^+,\lambda)$).
In order to bloom a $\lambda$-distributive tree from it, there is a need for a toolbox, each tool taking an abstract square-like sequence and producing a sequence which is slightly better than the original one.
For this, we introduce the monoid of postprocessing functions and study how it acts on the class of abstract square sequences.
We establish that, assuming GCH, the monoid contains some very powerful functions. We also prove that the monoid is closed under various mixing operations.
This allows us to prove a theorem which is just one step away from verifying the conjecture:

Theorem 1. Assume GCH and that $\lambda$ is a singular cardinal.
If $\square(\lambda^+,<\lambda)$ holds, then there exists a $\lambda$-distributive $\lambda^+$-Aronszajn tree.
Another proof, involving a 5-steps chain of applications of postprocessing functions, is of the following theorem.

Theorem 2. Assume GCH. If $\lambda$ is a singular cardinal and $\square(\lambda^+)$ holds, then there exists a $\lambda^+$-Souslin tree which is coherent mod finite.

This is joint work with Ari Brodsky. See: http://assafrinot.com/paper/29
It is well-known that the statement "all $\aleph_1$-Aronszajn trees are special'' is consistent with ZFC (Baumgartner, Malitz, and Reinhardt), and even with ZFC+GCH (Jensen). In contrast, Ben-David and Shelah proved that, assuming GCH, for every singular cardinal $\lambda$: if there exists a $\lambda^+$-Aronszajn tree, then there exists a non-special one. Furthermore:
Theorem (Ben-David and Shelah, 1986) Assume GCH and that $\lambda$ is singular ...

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## Faà di Bruno Hopf algebras, Dyson-Schwinger equations, and Lie-Butcher series.Based on a conference hosted by IRMAStrasbourg # June 27- July 1, 2011 Ebrahimi-Fard, Kurusch ; Fauvet, Frédéric | European Mathematical Society 2015

Congrès

- vi; 458 p.
ISBN 978-3-03719-143-9

IRMA lectures in mathematics and theoretical physics , 0021

Localisation : Colloque 1er étage (STRA)

algèbre de Hopf # analyse combinatoire # algèbre de Lie # opérateur non linéaire # arbre

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## Operads 2009Marseille # april 20-25, 2009 Loday, Jean-Louis ; Vallette, Bruno | Société Mathématique de France 2013

Congrès

- xvi; 279 p.
ISBN 978-2-85629-363-8

Séminaires & congrès , 0026

Localisation : Collection 1er étage

Actions naturelles # algèbres de Hopf # algèbres de Lie tordues # algèbres pré-Lie # algèbre dendriforme # algorithme de Buchberger # bases de Gröbner # catégories d'arbres # catégories de Koszul # catégorification # cohomologie de Hochschild # complétion de Knuth-Bendix # confluence # co-opérade de Poisson # diagrammes de flux et de programmation # enchevêtrement # espaces de configurations # foncteur de Schur # forme canonique # Haskell # Homologie des E_n-algèbres # identités entre les relations # méthodes de renormalisation perturbatives # n-catégorie # opérade # opérade des petits disques # polygraphe # pro # prop # présentation par générateurs et relations # réécriture # réécriture de diagrammes # renormalisation # S-modules # théorèmes de PBW # théorèmes libres # théorie algébrique # treillis de Tamari # tresse # type de dérivation fini Actions naturelles # algèbres de Hopf # algèbres de Lie tordues # algèbres pré-Lie # algèbre dendriforme # algorithme de Buchberger # bases de Gröbner # catégories d'arbres # catégories de Koszul # catégorification # cohomologie de Hochschild # complétion de Knuth-Bendix # confluence # co-opérade de Poisson # diagrammes de flux et de programmation # enchevêtrement # espaces de configurations # foncteur de Schur # forme canonique # Haskell # ...

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## Graph partitioning and graph clustering.10th DIMACS implementation challenge workshopAtlanta # February 13-14, 2012 Bader, David A. ; Meyerhenke, Henning ; Sanders, Peter ; Wagner, Dorothea | American Mathematical Society;Center for discrete mathematics and theoretical computer science 2013

Congrès

- xiii; 240 p.
ISBN 978-0-8218-9038-7

Contemporary mathematics , 0588

Localisation : Collection 1er étage

combinatoires # arbres # hypergraphe # factorisation # algorithme

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## Probability and real trees.Ecole d'été de probabilités de Saint-Flour XXXV-2005 Evans, Steven N. | Springer 2008

Congrès

- xi; 193 p.
ISBN 978-3-540-74797-0

Lecture notes in mathematics , 1920

Localisation : Collection 1er étage

arbre aléatoire # propriété asymptotique # convergence de mesure de probabilité # distance de Gromov-Hausdorff # forme de Dirichlet

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## Groups, Rings and Group Rings : International Conference Groups, Rings and Group RingsUbatuba # July 28- August 2, 2008 Giambruno, Antonio ; Polcino Milies, César ; Sehgal, Sudarshan K. | American Mathematical Society 2009

Congrès

- VII-270 p.
ISBN 978-0-8218-4771-8

Contemporary mathematics , 0499

Localisation : Collection 1er étage

théorie des groupes # anneaux de groupes # anneau # identité polynomiale # algèbre de Lie # superalgèbre

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## Harmonic analysis, signal processing, and complexity :festschrift in honr of the 60th birthday of Carlos A. Berenstein#May Sabadini, Irène ; Struppa, Danièle C. ; Walnut, David F. | Birkhäuser 2005

Congrès

- 162 p.
ISBN 978-0-8176-4358-4

Progress in mathematics , 0238

Localisation : Collection 1er étage

analyse harmonique # traitement du signal # complexité calculatoire # problème de Cauchy #idéal arithmétique # idéal analytique # EDP # opérateur d'Hermite # groupe d'Heisenberg # fonction subharmonique # structure discrète # variété hyperbolique # condition de Phragmen-Lindelöf # déconvolation locale # projection orthogonale # espace hyperbolique # ondelette

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## Bioconsensus :DIMACS working group meetings on bioconsensus#Oct. 25-26 and Oct. 2-5 Janowitz, M. F. ; Lapointe, F. J. ; McMorris, F. R. | American Mathematical Society 2003

Congrès

- 242 p.
ISBN 978-0-8218-3197-7

DIMACS series in discrete mathematics and theorerical computer science , 0061

Localisation : Collection 1er étage

biomathématique # mathématique appliquée à la biologie # arbre # bioconsensus # hypergraphe # ensemble ordonnée # classification # préférence de groupe # science comportementale # taxonomie # biologie moléculaire # évolution

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## Séminaire lotharingien de combinatoire31è session Oct. 17-20 Zeng, Jiang | IRMA 1994

Congrès

- 126 p.

Localisation : Salle de manutention

fonction de Schur # fonction symétrique # identite cyclotomique # matroïdes # mot de Motzkin # nombre d

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## Microsurveys in discrete probability :DIMACS workshop#June 2-6 Aldous, David ; Propp James | American Mathematical Society 1998

Congrès

- 220 p.
ISBN 978-0-8218-0827-6

DIMACS series in discrete mathematics and theoretical computer science , 0041

Localisation : Collection 1er étage

arborescence # chaine de Markov # combinatoire # probabilité # théorie des graphes

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## Networks in distributed computing :Dimacs workshop held at rutgers university#Oct. 27-29 Mavronicolas, Marios ; Merritt, Michael ; Shavit, Nir | American Mathematical Society 1999

Congrès

- 160 p.
ISBN 978-0-8218-0992-1

DIMACS series in discrete mathematics and theoretical computer science , 0045

Localisation : Collection 1er étage

algorithme # analyse # application # combinatoire # cryptographie # graphe # industrie # mathématique appliquée # mobile # passage # protocole réseau # réseau ATM # réseau de communication # réseau radio # système distribué # théorie des graphes # traitement des données # électronique

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## TreesworkshopVersaillesJune 14-16 Chauvin, Brigitte ; Cohen, Serge ; Rouault, Alain | Birkhäuser Verlag 1996

Congrès

ISBN 978-3-7643-5453-4

Progress in probability , 0040

Localisation : Colloque 1er étage (PARI)

arborescence # arbre # arbre continu # combinatoire # informatique algorithme # martingale # physique statistique # probabilité # processus de Markov # processus markovien de branchement # structure géométrique # théorie des graphes

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## Séminaire lotharingien de combinatoire(Bayreuth, Erlangen, Strasbourg)28e session Zeng, Jiang | CNRS;Publication de l'IRMA;Universite Louis Pasteur 1992

Congrès

Publication de l'IRMA, Strasbourg

Localisation : Colloque 1er étage (OTTR)

arbre évolutionaire # chemin de Motzkin # déterminant de Hankel # fonction de Schur # fonction symétrique # identité de caractères # moment # partition # permutation # polynômes de Witt # q-analogues # sommation hypergéométrique # tableau semi-standard

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## Graph theory and sparse matrix computation George, Alan ; Gilbert, John R. ; Liu, Joseph W.H. | Springer-Verlag 1993

Congrès

- 245 p.
ISBN 978-0-387-94131-8

The IMA volumes in mathematics and its applications , 0056

Localisation : Colloque 1er étage (MINN)

algèbre linéaire numérique # calcul des matrices # factovisation des matrices # mathématique discrète # méthode itérative # orthogonalisation # système surdéterminé # théorie des graphs

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## Séminaire lotharingien de combinatoire(Bayreuth, Erlangen,Strasbourg) 28e session Zeng, Jiang | IRMA;ULP 1992

Congrès

- 143 p.

Publication de l'IRMA , 498

Localisation : Salle de manutention

analogue # chemins de Motzkin # déterminants de Hankel # evolutionary trees # fonction symétrique # fonctions de Schur # identité de caractères # moments # partition # permutation # polynômes de Witt # sommation hypergéométrique # tableaux semi-standard

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## Condensation in random trees 3/3 Kortchemski, Igor | CIRM H

Multi angle

Research schools

We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms for instance connected with data allocation), combinatorics (trees are combinatorial objects by essence), mathematical genetics (as phylogenetic trees), in statistical physics (for instance in connection with random maps as we will see below) and in probability theory (where trees describe the genealogical structure of branching processes, fragmentation processes, etc.). We shall specifically focus on Bienaymé-Galton-Watson trees (which is the simplest
possible genealogical model, where individuals reproduce in an asexual and stationary way), whose offspring distribution is subcritical and is regularly varying. The main tool is to code these trees by integer-valued random walks with negative drift, conditioned on a late return to the origin. The study of such random walks, which is of independent interest, reveals a "one-big jump principle" (identified by Armendáriz & Loulakis in 2011), thus explaining the condensation phenomenon.

Section 1 gives some history and motivations for studying Bienaymé-Galton-Watson trees.
Section 2 defines Bienaymé-Galton-Watson trees.
Section 3 explains how such trees can be coded by random walks, and introduce several useful tools, such as cyclic shifts and the Vervaat transformation, to study random walks under a conditioning involving positivity constraints.
Section 4 contains exercises to manipulate connections between BGW trees and random walks, and to study ladder times of downward skip-free random walks.
Section 5 gives estimates, such as maximal inequalities, for random walks in order to establish a "one-big jump principle".
Section 6 transfers results on random walks to random trees in order to identity the condensation phenomenon.

The goal of these lecture notes is to be as most self-contained as possible.
We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms ...

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## Condensation in random trees 2/3 Kortchemski, Igor | CIRM H

Multi angle

Research schools

We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms for instance connected with data allocation), combinatorics (trees are combinatorial objects by essence), mathematical genetics (as phylogenetic trees), in statistical physics (for instance in connection with random maps as we will see below) and in probability theory (where trees describe the genealogical structure of branching processes, fragmentation processes, etc.). We shall specifically focus on Bienaymé-Galton-Watson trees (which is the simplest
possible genealogical model, where individuals reproduce in an asexual and stationary way), whose offspring distribution is subcritical and is regularly varying. The main tool is to code these trees by integer-valued random walks with negative drift, conditioned on a late return to the origin. The study of such random walks, which is of independent interest, reveals a "one-big jump principle" (identified by Armendáriz & Loulakis in 2011), thus explaining the condensation phenomenon.

Section 1 gives some history and motivations for studying Bienaymé-Galton-Watson trees.
Section 2 defines Bienaymé-Galton-Watson trees.
Section 3 explains how such trees can be coded by random walks, and introduce several useful tools, such as cyclic shifts and the Vervaat transformation, to study random walks under a conditioning involving positivity constraints.
Section 4 contains exercises to manipulate connections between BGW trees and random walks, and to study ladder times of downward skip-free random walks.
Section 5 gives estimates, such as maximal inequalities, for random walks in order to establish a "one-big jump principle".
Section 6 transfers results on random walks to random trees in order to identity the condensation phenomenon.

The goal of these lecture notes is to be as most self-contained as possible.
We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Condensation in random trees 1/3 Kortchemski, Igor | CIRM H

Multi angle

Research schools

We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms for instance connected with data allocation), combinatorics (trees are combinatorial objects by essence), mathematical genetics (as phylogenetic trees), in statistical physics (for instance in connection with random maps as we will see below) and in probability theory (where trees describe the genealogical structure of branching processes, fragmentation processes, etc.). We shall specifically focus on Bienaymé-Galton-Watson trees (which is the simplest
possible genealogical model, where individuals reproduce in an asexual and stationary way), whose offspring distribution is subcritical and is regularly varying. The main tool is to code these trees by integer-valued random walks with negative drift, conditioned on a late return to the origin. The study of such random walks, which is of independent interest, reveals a "one-big jump principle" (identified by Armendáriz & Loulakis in 2011), thus explaining the condensation phenomenon.

Section 1 gives some history and motivations for studying Bienaymé-Galton-Watson trees.
Section 2 defines Bienaymé-Galton-Watson trees.
Section 3 explains how such trees can be coded by random walks, and introduce several useful tools, such as cyclic shifts and the Vervaat transformation, to study random walks under a conditioning involving positivity constraints.
Section 4 contains exercises to manipulate connections between BGW trees and random walks, and to study ladder times of downward skip-free random walks.
Section 5 gives estimates, such as maximal inequalities, for random walks in order to establish a "one-big jump principle".
Section 6 transfers results on random walks to random trees in order to identity the condensation phenomenon.

The goal of these lecture notes is to be as most self-contained as possible.
We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random discrete structures as their size grows. Trees appear in many different areas such as computer science (where trees appear in the analysis of random algorithms ...

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## Shuffles of trees Hoffbeck, Eric | CIRM H

Multi angle

Research talks;Combinatorics;Topology

We study a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets. We give several equivalent descriptions of the shuffles, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. This is a joint work with Ieke Moerdijk. We study a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets. We give several equivalent descriptions of the shuffles, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. This is a ...

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