Related papers: Hiding Quiet Solutions in Random Constraint Satisf…
The phase transitions of random-field q-state Potts models in d=3 dimensions are studied by renormalization-group theory by exact solution of a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions of a cubic…
An analysis of the random lattice gas in the annealed limit is presented. The statistical mechanics of disordered lattice systems is briefly reviewed. For the case of the lattice gas with an arbitrary uniform interaction potential and…
In this note we show that local equilibrium equations (the generalization of the TAP equations or of the belief propagation equations) do have solutions in the colorable phase of the coloring problem. The same results extend to other…
From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…
The focus of this thesis is about statistical mechanics on heterogeneous random graphs, i.e. how this heterogeneity affects the cooperative behavior of model systems. It is not intended as a review on it, rather it is showed how this…
Within the framework of generalized combinatorial approach, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With…
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming…
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…
Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We present a study of the coloring problem (antiferromagnetic Potts model) of random regular graphs, submitted to quantum fluctuations induced by a transverse field, using the quantum cavity method and quantum Monte-Carlo simulations. We…
We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random…
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…
Local constraints play an important role in the effective description of many quantum systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. We develop a large $N$ diagrammatic formalism to…