Consider a lattice gas evolving according to the conservative Kawasaki dynamics at inverse temperature on a two dimensional torus . We prove the tunneling behavior of the process among the states of minimal energy. More precisely, assume that there are particles, , and that the initial state is the configuration in which all sites of the square are occupied. We show that in the time scale the process evolves as a Markov process on which jumps from any site to any other site at a strictly positive rate which can be expressed in terms of the hitting probabilities of simple Markovian dynamics.
On considère un gaz sur réseau évoluant selon la dynamique de Kawasaki à température inverse sur le tore bi-dimensionel . Nous étudions l’évolution du processus parmi les états d’énergie minimale. Supposons la présence de particules, et qu’á l’état initial les sites du carré soient tous occupés. Nous montrons qu’á l’échelle de temps le processus évolue comme une chaîne de Markov sur qui saute d’un site vers un site à un taux strictement positif qui peut-être exprimé en terme de probabilités d’atteinte de dynamiques markoviennes élémentaires.
Keywords: metastability, tunneling, lattice gases, kawasaki dynamics, capacities
@article{AIHPB_2015__51_1_59_0, author = {Beltr\'an, J. and Landim, C.}, title = {Tunneling of the {Kawasaki} dynamics at low temperatures in two dimensions}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {59--88}, publisher = {Gauthier-Villars}, volume = {51}, number = {1}, year = {2015}, doi = {10.1214/13-AIHP568}, mrnumber = {3300964}, zbl = {06412898}, language = {en}, url = {http://www.numdam.org/articles/10.1214/13-AIHP568/} }
TY - JOUR AU - Beltrán, J. AU - Landim, C. TI - Tunneling of the Kawasaki dynamics at low temperatures in two dimensions JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 59 EP - 88 VL - 51 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/13-AIHP568/ DO - 10.1214/13-AIHP568 LA - en ID - AIHPB_2015__51_1_59_0 ER -
%0 Journal Article %A Beltrán, J. %A Landim, C. %T Tunneling of the Kawasaki dynamics at low temperatures in two dimensions %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 59-88 %V 51 %N 1 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/13-AIHP568/ %R 10.1214/13-AIHP568 %G en %F AIHPB_2015__51_1_59_0
Beltrán, J.; Landim, C. Tunneling of the Kawasaki dynamics at low temperatures in two dimensions. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, pp. 59-88. doi : 10.1214/13-AIHP568. http://www.numdam.org/articles/10.1214/13-AIHP568/
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