Related papers: Stability for a continuous SOS-interface model in …
We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new…
We propose a new type of SPDEs, singular or with regularized noises, motivated by a study of the fluctuation of the density field in a microscopic interacting particle system. They include a large scaling parameter $N$, which is the ratio…
We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…
We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…
We study the interface of the Ising model in a box of side-length $n$ in $\mathbb Z^3$ at low temperature $1/\beta$ under Dobrushin's boundary conditions, conditioned to stay in a half-space above height $h$ (a hard floor). Without this…
We consider the disordered monomer-dimer model on cylinder graphs $\mathcal{G}_n$, i.e., graphs given by the Cartesian product of the line graph on $n$ vertices, and a deterministic graph. The edges carry i.i.d. random weights, and the…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent \nu. This class…
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
The Gibbs measures of a spin system on $Z^d$ with unbounded pair interactions $J_{xy} \sigma (x) \sigma (y)$ are studied. Here $\langle x, y \rangle \in E $, i.e. $x$ and $y$ are neighbors in $Z^d$. The intensities $J_{xy}$ and the spins…
The refined de Sitter (dS) conjecture provides two consistency conditions for an effective theory potential of a quantum gravity theory. Any inflationary model can be checked by these conditions and minimal gauge inflation is not an…
We analyze the Block Averaging Transformation applied to the two--dimensional Ising model in the uniqueness region. We discuss the Gibbs property of the renormalized measure and the convergence of renormalized potential under iteration of…
We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
Chaotic dependence on temperature refers to the phenomenon of divergence of Gibbs measures as the temperature approaches a certain value. Models with chaotic behaviour near zero temperature have multiple ground states, none of which are…