Related papers: Central Approximation in Statistical Physics and I…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g.,…
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(n,a), defined as the number of decompositions of a positive integer 'n'…
Particle statistics is a fundamental part of quantum physics, and yet its role and use in the context of quantum information have been poorly explored so far. After briefly introducing particle statistics and the Symmetrization Postulate, I…
Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP…
We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators…
We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the…