相关论文: Limit laws for boolean convolutions
Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…
We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020),…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
We investigate the rate of convergence toward the Boolean extreme value distribution, which is the universal limiting law for the normalized spectral maximum of Boolean independent and identically distributed positive operators, under the…
We formulate and establish the central limit theorem for products of i.i.d. random variables on arbitrary simply connected nilpotent Lie groups, allowing a possible bias. Two new phenomena arise in the presence of a bias: (a) the walk…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth…
We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show…
Let $\{X_{i,j}:(i,j)\in\mathbb N^2\}$ be a two-dimensional array of independent copies of a random variable $X$, and let $\{N_n\}_{n\in\mathbb N}$ be a sequence of natural numbers such that $\lim_{n\to\infty}e^{-cn}N_n=1$ for some $c>0$.…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
Consider two random variables following Skellam distributions of parameters going to infinity linearly. We prove that the limit distribution of the first variable, conditionally on being equal to the second, is Gaussian.
We give estimates on the rate of convergence in the Boolean central limit theorem for the L\'evy distance. In the case of measures with bounded support we obtain a sharp estimate by giving a qualitative description of this convergence.
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
Research in quantitative evolutionary genomics and systems biology led to the discovery of several universal regularities connecting genomic and molecular phenomic variables. These universals include the log-normal distribution of the…
We prove the existence of a limit of the finite volume probability measures generated by tree growth rules in Ford's alpha model of phylogenetic trees. The limiting measure is shown to be concentrated on the set of trees consisting of…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
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…