m
• E

F Nous contacter

0

# Documents  82C43 | enregistrements trouvés : 9

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 1 Seppäläinen, Timo | CIRM H

Post-edited

Research School;Mathematical Physics;Probability and Statistics

Variational formulas for limit shapes of directed last-passage percolation models. Connections of minimizing cocycles of the variational formulas to geodesics, Busemann functions, and stationary percolation.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Probability and statistical physics in St. Petersburg.St. Petersburg school on probability and statistical physicsSt. Petersburg # June 18-29, 2012 Sidoravicius, V. ; Smirnov, S. | American Mathematical Society 2016

Congrès

- vi; 471 p.
ISBN 978-1-4704-2248-6

Proceedings of symposia in pure mathematics , 0091

Localisation : Collection 1er étage

probabilités # physique statistique # théorie ergodique # marche aléatoire # chaîne de Markov # modèle de Potts # mesure invariante # champ Gaussien

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Multi-time distribution of periodic TASEP Baik, Jinho | CIRM H

Multi angle

Research talks;Mathematical Physics;Probability and Statistics

We consider periodic TASEP with periodic step initial condition, and evaluate the joint distribution of the locations of m particles. For arbitrary indices and times, we find a formula for the multi-time, multi-space joint distribution in terms of an integral of a Fredholm determinant. We then discuss the large time limit in the so-called relaxation scale. The one-point distributions for other initial conditions are also going to discussed.
Based on joint work with Zhipeng Liu (NYU).
We consider periodic TASEP with periodic step initial condition, and evaluate the joint distribution of the locations of m particles. For arbitrary indices and times, we find a formula for the multi-time, multi-space joint distribution in terms of an integral of a Fredholm determinant. We then discuss the large time limit in the so-called relaxation scale. The one-point distributions for other initial conditions are also going to discus...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The KPZ fixed point - Lecture 2 Remenik, Daniel | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion process (TASEP). Then I will present a Fredholm determinant formula for its distribution (at a fixed time) and show how all the main properties of the fixed point (including the Markov property, space and time regularity, symmetries and scaling invariance, and variational formulas) can be derived from the formula and the construction, and also how the formula reproduces known self-similar solutions such as the $Airy_1andAiry_2$ processes.
The second part of the course will be devoted to explaining how the KPZ fixed point can be computed starting from TASEP. The method is based on solving, for any initial condition, the biorthogonal ensemble representation for TASEP found by Sasamoto '05 and Borodin-Ferrari-Prähofer-Sasamoto '07. The resulting kernel involves transition probabilities of a random walk forced to hit a curve defined by the initial data, and in the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a Fredholm determinant formula given in terms of analogous kernels based on Brownian motion.
Based on joint work with K. Matetski and J. Quastel.
In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The KPZ fixed point - Lecture 1 Remenik, Daniel | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion process (TASEP). Then I will present a Fredholm determinant formula for its distribution (at a fixed time) and show how all the main properties of the fixed point (including the Markov property, space and time regularity, symmetries and scaling invariance, and variational formulas) can be derived from the formula and the construction, and also how the formula reproduces known self-similar solutions such as the $Airy_1andAiry_2$ processes.
The second part of the course will be devoted to explaining how the KPZ fixed point can be computed starting from TASEP. The method is based on solving, for any initial condition, the biorthogonal ensemble representation for TASEP found by Sasamoto '05 and Borodin-Ferrari-Prähofer-Sasamoto '07. The resulting kernel involves transition probabilities of a random walk forced to hit a curve defined by the initial data, and in the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a Fredholm determinant formula given in terms of analogous kernels based on Brownian motion.
Based on joint work with K. Matetski and J. Quastel.
In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 3 Seppäläinen, Timo | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

Kardar-Parisi-Zhang fluctuation exponent for the last-passage value of the two-dimensional corner growth model with exponential weights. We sketch the proof of the fluctuation exponent for the stationary corner growth process, and if time permits indicate how the exponent is derived for the percolation process with i.i.d. weights.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 2 Seppäläinen, Timo | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

Busemann functions for the two-dimensional corner growth model with exponential weights. Derivation of the stationary corner growth model and its use for calculating the limit shape and proving existence of Busemann functions.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Scaling limits of interacting particle systems Kipnis, Claude ; Landim, Claudio | Springer 1999

Ouvrage

- 442 p.
ISBN 978-3-540-64913-7

Grundlehren der mathematischen wissenschaften , 0320

Localisation : Collection 1er étage

physique mathématique # système de particule # physique statistique # probability # processus de Markov # hydrodynamique # grande déviation

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Foundations of probability with applications :Selected papers 1974-1995 Suppes, Patrick ; Zanotti, Mario | Cambridge University Press 1996

Ouvrage

- 192 p.
ISBN 978-0-521-56835-7

Cambridge studies in probability, induction, and decision theory

Localisation : Ouvrage RdC (SUPP)

causalité # induction # mécanique quantique # probabilité # théorie de décision # épistémologie

#### Filtrer

##### Codes MSC

Ressources Electroniques (Depuis le CIRM)

Books & Print journals

Recherche avancée

0
Z