Abstract: Let n particles be independently allocated into N boxes, where the l-th box appears with the probability al. Let μr be the number of boxes with exactly r particles and μ = [μr1 , . . . , μrm ]. Asymptotical behavior of such random variables as N tends to infinity was studied by many authors. It was previously known that ifNal are all upper bounded and n/N is upper and lower bounded by...

This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio’s riskiness, if expectations of these risks are infinite. On the contrary, for concave functions of heavy-tailed risks with finite expectations, the stylized fact that diversification ...

This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...

In this paper we study several aspects of the growth of a supercritical Galton–Watson process {Zn :n ≥ 1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Zn, that is, the behavior of P (Zn = vn) as vn ր ∞, and use this to study conditional large deviations of {YZn :n ≥ 1}, where Yn satisfies an LDP, particularly of {Z −1 n Zn+1...

Let (X t , t ≥ 0) be a continuous time simple random walk on Z d , and let l T (x) be the time spent by (X t , t ≥ 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I T = x∈Z d l T (x) q in the critical dimension d = 2q q−1. When q is integer, we obtain similar results for the intersection local times of q independent simple random ...

Beginning with the pioneering efforts of Rubin et al. (1976), the study of large–scale deviations from Hubble flow has achieved undeniable observational successes (see reviews by Dekel 1994, Strauss and Willick 1995). In the spirit of providing fertile ground for discussion and further developments, this presentation will concentrate on few of the areas where a measure of variance of opinion ex...

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a one-dimensional setting, allowing reasonable run time and memory consu...

We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and...