Exact Simulation for Discrete Time Spin Systems and Unilateral Fields

Developments in Perfect Simulation of Gibbs Measures Through a New Result for the Extinction of Galton-Watson-Like Processes

“…Note that in literature more general definitions of interactions are considered but in our paper we will only use this more restrictive definition, as done also in [3]. For brevity of notation set χ B (σ ) = v∈B σ (v) for any B Z d and σ ∈ S. A probability measure π on (S, S) is said to be a Gibbs measure relative to the interaction J ∈ J if for all v ∈ Z d and for any ζ ∈ S π σ (v) = ζ(v)|σ (u) = ζ(u) ∀u = v = 1 1 + exp(−2 B: v∈B (J B χ B (σ ))) a.s. (2) which are called local specifications. Let us define the set A v = {B Z d : v ∈ B, J B = 0}, for v ∈ Z d ; the set A v is finite or countable, therefore we can write…”

“…then there exists a unique Gibbs measure verifying the local specifications (see (2)). Therefore (H2) can be seen also as a sufficient condition for the uniqueness of the Gibbs measure.…”

One-Dimensional Infinite Memory Imitation Models with Noise

“…For perfect simulation in the multi-dimensional case the reader is addressed to e.g. [5,7,15]; also the continuity assumption can be relaxed, as in [6].…”

Backward Coalescence Times for Perfect Simulation of Chains with Infinite Memory

“…In [13] a stochastic recursive sequence for perfect simulation was constructed, called the gamma coupler, for transition kernels satisfying a minorization condition. We also mention the area of perfect simulation devoted to spatial contexts, such as stochastic geometry [6], [12] and random fields [3], [11].…”