Related papers: Spatial random permutations with small cycle weigh…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Consider a model of $N$ independent, increasing $\mathbb{N}_0$-valued processes, with random, independent waiting times between jumps. It is known that there is either an emergent `leader', in which a single process possesses the maximal…
In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the…
We derive bounds on the number of switches at an arbitrary set of positions in a circular sequence of permutations and relate them to the diameter of Multipermutohedra.
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…
Two permutations are similar if they have the same length and the same relative order. A collection of $r\ge2$ disjoint, similar subsequences of a permutation $\pi$ form $r$-twins in $\pi$. We study the longest guaranteed length of…
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future…
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted…
We study perpetuities of a special type related to the size-biased distributions. Necessary and sufficient conditions of their existence and uniqueness are obtained. A crucial point in proving all results is a close connection between…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Telescoping sums very naturally lead to probability distributions on ${\mathbb Z}^+$. But are these distributions typically cosmetic and devoid of motivation? In this paper we give three examples of "first occurrence" distributions, each…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
We study joint distributions of cycles and patterns in permutations written in standard cycle form. We explore both classical and generalised patterns of length 2 and 3. Many extensions of classical theory are achieved; bivariate generating…
The large scale gravitational potential distribution and its influence on the large-scale matter clustering is considered on the basis of six simulations. It is found that the mean separation between zero levels of the potential along…