相关论文: Elementary Proofs of the Main Limit Theorems of Pr…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the…
We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel…
The Max-Min and Min-Max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the Max-Min and Min-Max is challenging as matrices are large and full information about their…
The purpose of this paper is to study the limiting distribution of special {\it additive functionals} on random planar maps, namely the number of occurrences of a given {\it pattern}. The main result is a central limit theorem for these…
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be…
About 35 years ago Wheeler introduced the motto `law without law' to highlight the possibility that (at least a part of) Physics may be understood only following {\em regularity principles} and few relevant facts, rather than relying on a…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
In terms of the Dirac representation of sample mean and the weak convergence of empirical distributions that holds almost surely, we construct a new proof for a strong law of large numbers of Kolmogorov's type with i.i.d. random variables…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…