Related papers: Central Limit Theorems via Analytic Combinatorics …
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 introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
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 study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn.
We introduce new types of local algorithms, which we call "ASI Algorithms", and use them to demonstrate a link between descriptive and computable combinatorics. This allows us to unify arguments from the two fields, and also sometimes to…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by…
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
Analytic combinatorics in several variables refers to a suite of tools that provide sharp asymptotic estimates for certain combinatorial quantities. In this paper, we apply these tools to determine the Gilbert-Varshamov (GV) bound for the…
We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…
We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence. We give a simple combinatorial characterization of…
Cooperative constraint solving is an area of constraint programming that studies the interaction between constraint solvers with the aim of discovering the interaction patterns that amplify the positive qualities of individual solvers.…
We present a strategy for computing asymptotics of coefficients of $d$-variate algebraic generating functions. Using known constructions, we embed the coefficient array into an array represented by a rational generating functions in $d+1$…
A useful heuristic in the understanding of large random combinatorial structures is the Arratia-Tavare principle, which describes an approximation to the joint distribution of component-sizes using independent random variables. The…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…