Emilio De Santis

Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

AbstractWe consider stochastic processes,

Waiting for ABRACADABRA. Occurrences of Words and Leading Numbers

S^t \equiv (S_x^t :x \in \mathbb{Z}^d ) \in \mathcal{S}_0^{\mathbb{Z}^d }

Stochastic Ising model with flipping sets of spins and fast decreasing temperature

with

Backward coalescence times for perfect simulation of chains with infinite memory

\mathcal{S}_0

First occurrence of a word among the elements of a finite dictionary in random sequences of letters

finite, in which spin flips (i.e., changes of Stx) do not raise the energy. We extend earlier results of Nanda–Newman–Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.

Exact Simulation for Discrete Time Spin Systems and Unilateral Fields

In this paper we consider the problem of determining the law of binary stochastic processes from transition kernels depending on the whole past. These kernels are linear in the past values of the process. They are allowed to assume values close to both 0 and 1, preventing the application of usual results on uniqueness. We give sufficient conditions for uniqueness and non-uniqueness; in the former case a perfect simulation algorithm is also given.