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Documents  82D60 | enregistrements trouvés : 13

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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.

60K35 ; 60K37 ; 82C22 ; 82C43 ; 82D60

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V

- x; 186 p.
ISBN 978-0-8218-4466-3

Proceedings of symposia in applied mathematics , 0066

Localisation : Collection RdC

variétés # théorie des noeuds # ADN # biologie

53A04 ; 57M25 ; 57M27 ; 57R56 ; 81T45 ; 82D60 ; 92C40 ; 92E10

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V

- 215 p.
ISBN 978-0-387-98557-2

The IMA volumes in mathematics and its applications , 0102

Localisation : Congrès 1er étage (MINN/1996)

analyse numérique # mécanique statistique # structure de la matière # équilibre # méthode de Monte-Carlo # chaîne de Markov # polymère # somme de variables aléatoires indépendantes # marche aléatoire

82B41 ; 82B80 ; 60J15 ; 60J20 ; 82C41 ; 82C80 ; 82D60

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- 340 p.
ISBN 978-0-8218-3200-4

Contemporary mathematics , 0304

Localisation : Collection RdC

théorie des noeuds # mathématique de la physique # variété # complexe cellulaire # noeud en dimension 3 # entrelacs # mathématique appliquée # biologie # ADN # entrelacement

57-06 ; 57M25 ; 49Q10 ; 53A04 ; 57M27 ; 82D60 ; 82B41 ; 52C25 ; 53A30 ; 74C99

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y

Research talks

We study an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes an energy to the interaction Hamiltonian that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. We analyze the annealed free energy per monomer in the limit as the length of the polymer chain tends to infinity. We derive a spectral representation for the free energy and use this to show that there is a critical curve in the (charge bias, inverse temperature)-plane separating a ballistic phase from a subballistic phase. We show that the phase transition is first order, identify the scaling behaviour of the critical curve for small and for large charge bias, and also identify the scaling behaviour of the free energy for small charge bias and small inverse temperature. In addition, we prove a large deviation principle for the joint law of the empirical speed and the empirical charge, and derive a spectral representation for the associated rate function. This in turn leads to a law of large numbers and a central limit theorem. What happens for the quenched free energy per monomer remains open. We state two modest results and raise a few questions. Joint work with F. Caravenna, N. Petrelis and J. Poisat We study an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes an energy to the interaction Hamiltonian that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. We ...

82D60 ; 60K37 ; 60K35

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y

Research School

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 ...

82C31 ; 82C23 ; 82D60 ; 82C22 ; 82C43

... Lire [+]

y

Research School

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 ...

82C31 ; 82C23 ; 82D60 ; 82C22 ; 82C43

... Lire [+]

y

Research School

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.

60K35 ; 60K37 ; 82C22 ; 82C43 ; 82D60

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y

Research School

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.

60K35 ; 60K37 ; 82C22 ; 82C43 ; 82D60

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V

- 99 p.
ISBN 978-0-387-29167-3

The IMA volumes in mathematics and its applications , 0141

Localisation : Ouvrage Rdc (Mode)

mécanique des solides déformables # mécanique des fluides # mécanique statistique # mécanique des solides # rhéologie # polymère # modélisation # structure de la matière

74-06 ; 76-06 ; 82-06 ; 74AXX ; 76Axx ; 82D30 ; 82D60

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V

- xix; 635 p.
ISBN 978-0-521-87726-8

Localisation : Ouvrage RdC (TRAN)

analyse numérique # équation différentielle elliptique # équation différentielle parabolique

65Mxx ; 65-02 ; 35Lxx ; 65Y15 ; 76B15 ; 76N15 ; 76W05 ; 74C05 ; 76Mxx ; 82D60 ; 86A20

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V

- 362 p.
ISBN 978-3-540-58353-0

Localisation : Ouvrage RdC (OTTI)

mécanique des fluides # fluide visco-élastique # analyse stochastique # mécanique statistique # analyse numérique # polymer # dynamique des polymers # algorithme # simulation # FORTRAN # modélisation

76A10 ; 76M35 ; 82C80 ; 82D60

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V

- x; 379 p.
ISBN 978-0-19-850561-7

Oxford lecture series in mathematics and its applications , 0018

Localisation : Ouvrage RdC (JANS)

mécanique statistique # homogénéisation # matériau composite

82B41 ; 82-02 ; 82D60

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