Related papers: Local limit laws for symbol statistics in bicompon…

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…

The symbolic analytic spread of an ideal $I$ is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article we find upper bounds for the symbolic analytic spread under certain…

We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions.…

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities $\frac{a}{n}$ and $\frac{b}{n}$ respectively.…

Orthogonal statistical learning and double machine learning have emerged as general frameworks for two-stage statistical prediction in the presence of a nuisance component. We establish non-asymptotic bounds on the excess risk of orthogonal…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing…

In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…

We study random digraphs on sequences of expanders with bounded average degree {which converge locally in probability}. We prove that the threshold for the existence of a giant strongly connected component, as well as the asymptotic…

The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…

Language models are essentially probability distributions over token sequences. Auto-regressive models generate sentences by iteratively computing and sampling from the distribution of the next token. This iterative sampling introduces…

An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…

Surprisal theory has provided a unifying framework for understanding many phenomena in sentence processing (Hale, 2001; Levy, 2008a), positing that a word's conditional probability given all prior context fully determines processing…

Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the…

We consider a simplified model of the continuous double auction where prices are integers varying from $1$ to $N$ with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is…

We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the…

The explanations of large language models have recently been shown to be sensitive to the randomness used for their training, creating a need to characterize this sensitivity. In this paper, we propose a characterization that questions the…

This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…