Related papers: Estimation of local microcanonical averages in two…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a…
We study the single-site approximation of the Perron-Frobenius equation for a coupled map lattice exhibiting a phase transition at a critical value g_c of the coupling constant. We found that the critical exponents are the same as in the…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models…
Expectation value of dynamical variables in thermodynamically equilibrium state can be typically provided through well-known canonical average. The average includes tremendous number of possible states considered far beyond practically…
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation…
A coupling-constant definition is given based on the compositeness property of some particle states with respect to the elementary states of other particles. It is applied in the context of the vector-spin-1/2-particle interaction vertices…
By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…
Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Mat\'ern case, this class allows a continuous parameterization of…
We present a general method to compute canonical averages for physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO). First, we introduce a histogram reweighting scheme applicable to QUBO-based…
Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large…