相关论文: Limit laws for boolean convolutions

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of $d$ base $B$ being…

In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…

In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…

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.…

We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to…

This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…

We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…

We study mixtures of free, monotone, and Boolean independence described by a directed graph $G = (V,E)$ in the context of $\mathcal{T}$-free convolutions of Jekel and Liu. We prove general limit theorems for the associated additive…

Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…

We study how Boolean cumulants can be used in order to address operations with freely independent random variables, particularly in connection to the $*$-distribution of the product of two selfadjoint freely independent random variables,…

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…

We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the…

We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…

Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…

This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…

Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional…

We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We…

We introduce the notion of operator-valued infinitesimal (OVI) independence for the Boolean and monotone cases. Then show that OVI Boolean (resp. monotone) independence is equivalent to the operator-valued Boolean (resp. monotone)…

We show that the laws of autocorrelations decay in texts are closely related to applicability limits of language models. Using distributional semantics we empirically demonstrate that autocorrelations of words in texts decay according to a…