相关论文: Cavity approach for real variables on diluted grap…

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…

The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare…

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We…

Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…

We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level…

We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations…

In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing…

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…

Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized…

We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us…

This thesis focuses on the XY model, the simplest vector spin model, used for describing numerous physical systems. It is studied for different sources of quenched disorder: random couplings, random fields, or both them. The belief…

We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…

The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal…

In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…

Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…

We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues…

We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a Jaynes-Cummings Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to…