Algebraic \(L^ 2\) decay of attractive critical processes on the lattice
type: Item
instance of: scholarly article
title: Algebraic \(L^ 2\) decay of attractive critical processes on the lattice
zbMATH Open document ID: 0811.60089
author: Jean-Dominique Deuschel
published in: The Annals of Probability
publication date: 1995-05-02T00:00:00Z
review text: The algebraic decay and convergence in \(L^ 1\) \((L^ p)\) is investigated for a class of linear attractive processes which are described using a transient random walk. The dependence of the decay of \(\| P_ t f-\langle f\rangle\|_ p\) on the dimension as well as on the locality of the function \(f\) is studied. Both the estimates from below and from above are obtained. These results are applied to interacting Ornstein-Uhlenbeck processes, a branching random walk, and the ``stepping stone'' models. The last section is devoted to processes described by the use of a product measure (independent random walk) instead of the transient random walk.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 567185
zbMATH Keywords: interacting particle system
zbMATH Keywords: algebraic rate of convergence
zbMATH Keywords: critical branching random walk
zbMATH Keywords: critical Ornstein-Uhlenbeck process
zbMATH Keywords: linear attractive processes
zbMATH Keywords: interacting Ornstein-Uhlenbeck processes
reviewed by: Petr Holický
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988859
OpenAlex ID: W2049906464
DOI: 10.1214/AOP/1176988859
description: scientific article; zbMATH DE number 567185