Random-cluster dynamics in $\mathbb{Z}^{2}$: Rapid mixing with general boundary conditions

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Glauber dynamics on nonamenable graphs: boundary conditions and mixing time

We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n. This implies that the mixing time grows at most linearly in n. Th...

متن کامل

Glauber Dynamics on Hyperbolic Graphs: Boundary Conditions and Mixing Time

We study a continuous time Glauber dynamics reversible with respect to the Ising model on hyperbolic graphs and analyze the effect of boundary conditions on the mixing time. Specifically, we consider the dynamics on an n-vertex ball of the hyperbolic graph H(v, s), where v is the number of neighbors of each vertex and s is the number of sides of each face, conditioned on having (+)-boundary. If...

متن کامل

Glauber dynamics on trees: Boundary conditions and mixing time†

We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the so-called Bethe approximation. Specifically, we show that spectral gap and the log-Sobolev constant of the Glauber dynamics for the Ising model on an n-vertex regular tree with (+)-boundary are bounded below by a constant independent of n at all temperatures and all ex...

متن کامل

Random cluster dynamics for the Ising model is rapidly mixing

We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 is bounded by a polynomial in the size of the underlying graph. As a consequence, the Swendsen-Wang algorithm for the ferromagnetic Ising model at any temperature has the same polynomial mixing time bound.

متن کامل

Burgers Equation with Random Boundary Conditions

We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The Annals of Applied Probability

سال: 2020

ISSN: 1050-5164

DOI: 10.1214/19-aap1505