We study the variational principle for some non-Gibbsian measures. We give a necessary and sufficient condition for the validity of the implication â€œzero relative entropy density implies commonâ€¦ (More)

We study the asymptotic behavior of the simple random walk on oriented versions of Z2. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, withâ€¦ (More)

In this monograph, we survey some key issues of the theory of Gibbsian and non-Gibbsian measures in finite-spin lattice systems. While non-Gibbsian measures are truly only the object of the lastâ€¦ (More)

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontalâ€¦ (More)

We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show thatâ€¦ (More)

We consider the evolution of an asymptotically decoupled probability measure Î½ on Ising spin configurations under a Glauber dynamics. We prove that for any t > 0, Î½t is asymptotically decoupled andâ€¦ (More)

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first showâ€¦ (More)

We study the asymptotic behavior of the simple random walk on oriented versions of Z. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, withâ€¦ (More)

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first showâ€¦ (More)

In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on Z2 in the generalized Gibbs context. We first recall a few features of the Dobrushinâ€¦ (More)