Related papers: Large deviation rate functions for the partition f…

We restate a process presented by Stanley as a technique to prove that there exists exactly one $d$-differential distributive lattice for any positive integer $d$. This process can be trivially extended to apply to distributive finitary…

We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…

We establish a large deviation principle (LDP) for probability graphons, which are symmetric functions from the unit square into the space of probability measures. This notion extends classical graphons and provides a flexible framework for…

In this paper we analyze the rate-distortion function R(D) achievable using linear codes over GF(q), where q is a prime number.

We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinatorial analysis. As a consequence, we obtain the generating…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…

We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic…

We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…

First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…

In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on $\mathbb{Z}^d$, in dimension $d\ge 5$, both in the upward and downward directions. The results are analogous to those we obtained for…

A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…

We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often…

We study large deviations for random walks on Lie groups defined by $\sigma_n^n = \exp(\frac1nX_1)\cdots\exp(\frac1nX_n)$, where $\{X_n\}_{n\geq1}$ is an i.i.d sequence of bounded random variables in the Lie algebra $\mathfrak{g}$. We…

We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…