Related papers: Local limit theorems and mod-phi convergence

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…

We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman…

We prove local regularity up to flat part of boundary, for certain classes of distributional solutions that are $L_{\infty}L^{3,q}$ with $q$ finite.

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…

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…

We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a…

Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We prove a local central limit theorem for "nonconventional" sums generated by some classes of sufficiently fast mixing sequences.

We propose a discrete analogue for the boundary local time of reflected diffusions in bounded Lipschitz domains. This discrete analogue, called the discrete local time, can be effectively simulated in practice and is obtained pathwise from…

We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature. The bounds we…

We prove large-data local stability theorems for several spin models in two dimensions.

This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the…

We provide lower and upper bounds on the minimum size of a maximum stable set over graphs of flag spheres, as a function of the dimension of the sphere and the number of vertices. Further, we use stable sets to obtain an improved Lower…

As black-box machine learning models grow in complexity and find applications in high-stakes scenarios, it is imperative to provide explanations for their predictions. Although Local Interpretable Model-agnostic Explanations (LIME) [22] is…

We show that the Bernoulli part extraction method can be used to obtain approximate forms of the local limit theorem for sums of independent lattice valued random variables, with effective error term, that is with explicit parameters and…