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New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree
In this paper we consider a model with nearest-neighbor interactions with spin space [0, 1] on Cayley trees of order k ⩾ 2. In Yu et al. (
2013 ), a... -
Asymptotic Behavior of Density in the Boundary-Driven Exclusion Process on the Sierpinski Gasket
We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the...
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A New Characterization of Endogeny
Aldous and Bandyopadhyay have shown that each solution to a recursive distributional equation (RDE) gives rise to a recursive tree process (RTP),...
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Time-time Covariance for Last Passage Percolation with Generic Initial Profile
We consider time correlation for KPZ growth in 1 + 1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with...
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Optimality Regions and Fluctuations for Bernoulli Last Passage Models
We study the sequence alignment problem and its independent version, the discrete Hammersley process with an exploration penalty. We obtain rigorous...
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On Julia Set and Chaos in p-adic Ising Model on the Cayley Tree
In this paper, we study the chaotic behavior of the p -adic Ising-Potts map** associated with the p -adic Ising model on the Cayley tree. As an...
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The Periodic Schur Process and Free Fermions at Finite Temperature
We revisit the periodic Schur process introduced by Borodin in 2007. Our contribution is threefold. First, we provide a new simpler derivation of its...
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KPZ Equation Limit of Stochastic Higher Spin Six Vertex Model
We consider the stochastic higher spin six vertex (SHS6V) model introduced by Corwin and Petrov (Commun. Math. Phys., 343 (2), 651–700
2016 ) with... -
Convergence of the Stochastic Six-Vertex Model to the ASEP
In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a...
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Weakly Asymmetric Bridges and the KPZ Equation
We consider the corner growth dynamics on discrete bridges from (0, 0) to (2 N , 0), or equivalently, the weakly asymmetric simple exclusion process...
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Legendre Duality of Spherical and Gaussian Spin Glasses
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between...
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On Descriptions of All Translation Invariant p−adic Gibbs Measures for the Potts Model on The Cayley Tree of Order Three
Unlike the real number field, a set of p −adic Gibbs measures of p −adic lattice models of statistical mechanics has a complex structure in a sense...
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On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree
In the present paper, we study a new kind of p -adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure . For such a model, we...
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Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors’...
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On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations
We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ⩾ 1. We reduce the problem...
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On Ising Model with Four Competing Interactions on Cayley Tree
In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of...