We study the problem of efficiently sampling k-colorings of bipartite graphs. We show that a class of markov chains cannot be used as efficient samplers. Precisely, we show that, for any k, 6 ≤ k ≤ n1/3− , > 0 fixed, almost every bipartite graph on n + n vertices is such that the mixing time of any ergodic markov chain asymptotically uniform on its k-colorings is exponential in n/k (if it is al...

This paper is part of an attempt to understand the speed of mixing and related statistical properties for chaotic dynamical systems. More precisely, we are interested in systems that are expanding or hyperbolic on large parts (though not necessarily all) of their phase spaces. A natural approach to this problem is to pick a suitable reference set, and to regard a part of the system as having “r...

For a general attractive Probabilistic Cellular Automata on SZ d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the in uence from the boundary for the invariant measures of the system restricted to nite boxes. For a class of re...

In this paper we define and study new directional Metropolis–Hastings algorithms that propose states in hyperplanes. Each iteration in directional Metropolis–Hastings algorithms consist of three steps. First a direction is sampled by an auxiliary variable. Then a potential new state is proposed in the subspace defined by this direction and the current state. Lastly, the potential new state is a...

We consider quadratic forms of martingale differences and establish a central limit theorem under mild and easily verifiable conditions+ By approximating Fourier transforms of stationary processes by martingales, our central limit theorem is applied to the smoothed periodogram estimate of spectral density functions+ Our results go beyond earlier ones by allowing a variety of nonlinear time seri...