Details

Autor(en) / Beteiligte

• Michelen, Marcus
• Perkins, Will

Titel

Strong Spatial Mixing for Repulsive Point Processes

Ist Teil von

• Journal of statistical physics, 2022-10, Vol.189 (1), Article 9

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We prove that a Gibbs point process interacting via a finite-range, repulsive potential ϕ exhibits a strong spatial mixing property for activities λ < e / Δ ϕ , where Δ ϕ is the potential-weighted connective constant of ϕ , defined recently in Michelen and Perkins ( http://arxiv.org/abs/2008.00972 , 2020). Using this we derive several analytic and algorithmic consequences when λ satisfies this bound: We prove new identities for the infinite volume pressure and surface pressure of such a process (and in the case of the surface pressure establish its existence). We prove that local block dynamics for sampling from the model on a box of volume N in R d mixes in time O ( N log N ) , giving efficient randomized algorithms to approximate the partition function and approximately sample from these models. We use the above identities and algorithms to give efficient approximation algorithms for the pressure and surface pressure.