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Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro CaputoPaolo Dai PraGustavo Posta — 2009

Annales de l'I.H.P. Probabilités et statistiques

We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...

Scaling limit and cube-root fluctuations in SOS surfaces above a wall

Pietro CaputoEyal LubetzkyFabio MartinelliAllan SlyFabio Lucio Toninelli — 2016

Journal of the European Mathematical Society

Consider the classical ( 2 + 1 ) -dimensional Solid-On-Solid model above a hard wall on an L × L box of 2 . The model describes a crystal surface by assigning a non-negative integer height η x to each site x in the box and 0 heights to its boundary. The probability of a surface configuration η is proportional to exp ( - β ( η ) ) , where β is the inverse-temperature and ( η ) sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough temperatures....

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