相关论文: Limit Theorem for Sums of Random Products
We generalise the Erdos-Renyi limit theorem on the maximum of the partial sums of random variables to the case when the number of terms in these sums is randomly distributed. Certain relations between the limiting theorems of this type and…
In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is…
In this paper the Random Energy Model(REM) under exponential type environment is considered which includes double exponential and Gaussian cases. Limiting Free Energy is evaluated in these models. Limiting Gibbs' distribution is evaluated…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
We study sums of a random multiplicative function; this is an example, of number-theoretic interest, of sums of products of independent random variables (chaoses). Using martingale methods, we establish a normal approximation for the sum…
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…
For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…
We bound an exponential sum that appears in the study of irregularities of distribution (the low-frequency Fourier energy of the sum of several Dirac measures) by geometric quantities: a special case is that for all $\left\{ x_1, \dots,…
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 determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. In the case of positive variables, the main theorem extends a result proved earlier for arrays with identically…
In this paper we establish functional Erd\H{o}s-Renyi laws for L\'evy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework,…
We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.
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…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
We prove entropic and total variation versions of the Erd\H{o}s-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
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…