Related papers: Exact solution of the random bipartite matching mo…
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
The estimation of rare event probabilities plays a pivotal role in diverse fields. Our aim is to determine the probability of a hazard or system failure occurring when a quantity of interest exceeds a critical value. In our approach, the…
We get back to the computation of the leading finite size corrections to some random link matching problems, first adressed by Mezard and Parisi [J. Physique 48 (1987) 1451-1459]. In the so-called bipartite case, their result is in…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the…
We consider a bipartite mean-field model in which both the interaction constant and the external field take different values only depending on the groups particles belong to. We compute the exact value of the thermodynamic limit of the…
In the absence of external driving, a system exposed to thermal fluctuations will relax to equilibrium. However, the constant input of work makes it possible to counteract this relaxation, and maintain the system in a nonequilibrium steady…
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using…
We consider a discrete-time bipartite matching model with random arrivals of units of supply and demand that can wait in queues located at the nodes in the network. A control policy determines which are matched at each time. The focus is on…
We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the…
Equilibrium free energy differences are given by exponential averages of nonequilibrium work values; such averages, however, often converge poorly, as they are dominated by rare realizations. I show that there is a simple and intuitively…
We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant.…
This paper presents a consensus algorithm for a multi-agent system where each agent has access to its imperfect own state and neighboring state measurements. The measurements are subject to deterministic disturbances and the proposed…
We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is…
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact…
In this work we theoretically study pairing in two-dimensional Fermi gases, a system which is experimentally accessible using cold atoms. We start by deriving the mean-field pairing gap equation for a coordinate-space potential with a…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibility. For the a posteriori error analysis we consider the…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…