Related papers: Local Limit Theorems in some Random models from Nu…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function…

For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…

We investigate the R\'enyi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the R\'enyi entropy, for Poisson-Bernoulli variables. As…

We present a generalization of Warning's Second Theorem to polynomial systems over a finite local principal ring with suitably restricted input and output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new…

In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$ and derive a Singleton-like bound for…

We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…

We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the large deviation regime for bounded additive functionals of…

The de Moivre-Laplace theorem is a special case of the central limit theorem for Bernoulli random variables, and can be proved by direct computation. We deduce the central limit theorem for any random variable with finite variance from the…

This article deals with limit theorems for certain loop variables for loop soups whose intensity approaches infinity. We first consider random walk loop soups on finite graphs and obtain a central limit theorem when the loop variable is the…

We study skew-products of the form (x,\omega)\mapsto (Tx, \omega+\phi(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \tilde\mu, and \phi:X\to S^1 is a C^1 function. Under mild…

We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive…

Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…

This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…

Let $S_n$ be a lattice random walk with mean zero and finite variance, and let $\Lambda^a_n$ be its occupation measure at level $a$. In this note, we prove local limit theorems for $\Pr[S_n=x,\Lambda^a_n=\ell]$ and…

The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are…

In this article we prove a general theorem which establishes the existence of limiting distributions for a wide class of error terms from prime number theory. As a corollary to our main theorem, we deduce previous results of Wintner (1935),…

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of…

The law of large numbers is one of the fundamental properties which algorithmically random infinite sequences ought to satisfy. In this paper, we show that the law of large numbers can be effectivized for an arbitrary Schnorr random…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…