We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum. New estimates for Glauber-type dynamics are also obtained.
Spectral gap estimates for interacting particle systems via a Bochner-type identity / A., Boudou; P., Caputo; P., Dai Pra; Posta, Gustavo; Rizzello, CARLO GIUSEPPE. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 232:(2006), pp. 222-258. [10.1016/j.bbr.2011.03.031]
Spectral gap estimates for interacting particle systems via a Bochner-type identity
POSTA, GUSTAVO;RIZZELLO, CARLO GIUSEPPE
2006
Abstract
We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum. New estimates for Glauber-type dynamics are also obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
