Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems

Details Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems

2002-11-06

arxiv.org/abs/math/0211108v1

Markov Processes and Related Fields 9, 3 (2003) 341-362

Mathematics

Probability

20 pages. Accepted for publication in ``Markov Processes and Related Fields''

Scientific paper

Inspired by the recent results of C. Landim, G. Panizo and H.-T. Yau [LPY] on spectral gap and logarithmic Sobolev inequalities for unbounded conservative spin systems, we study uniform bounds in these inequalities for Glauber dynamics of Hamiltonian of the form V(x_1) + ... + V(x_n) + V(M-x_1 -...-x_n), (x_1,...,x_n) in R^n Specifically, we examine the case V is strictly convex (or small perturbation of strictly convex) and, following [LPY], the case V is a bounded perturbation of a quadratic potential. By a simple path counting argument for the standard random walk, uniform bounds for the Glauber dynamics yields, in a transparent way, the classical L^{-2} decay for the Kawasaki dynamics on d-dimensional cubes of length L. The arguments of proofs however closely follow and make heavy use of the conservative approach and estimates of [LPY], relying in particular on the Lu-Yau martingale decomposition and clever partitionings of the conditional measure.

Affiliated with

Also associated with

No associations

Rating

Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Glauber versus Kawasaki for spectral gap and logarithmic Sobolev inequalities of some unbounded conservative spin systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448462