The number of fixed points of a random permutation of {1, 2, . . . , n} has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they are trivial – almost every permutation has no fixed points. For the usual actio...

This paper presents new random fixed point theorems and random Leray–Schauder alternatives for a variety of maps (e.g., Bκ, Uκ c , KKM and PK maps). A random Kransnoselskii cone compression theorem for Uκ c maps is also given. Various random approximation theorems for the above classes are proved and as applications several random fixed point theorems are also derived.

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

Abstract: We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and ...

Exploiting the empirical observation that the probability of k fixed points in a Welch Costas permutation is approximately the same as in a random permutation of the same order, we propose a stochastic model for the most probable maximal number of fixed points in a Welch Costas permutation.

Table A. ERGM Notations Network Graph Y, Yij a random network graph matrix, its i,j element Y-ij all elements except i,j y the set of all possible graphs for a fixed set of notes y, yij y, yij a realization of the random network graph and its i,j element zk(y) a statistic of network graph y Network Statistics t total number of edges d2 number of nodes which have at least 2 edges hs number of ed...

We consider the uniform generation of random derangements, i.e., permutations without any fixed point. By using a rejection algorithm, we improve the straight-forward method of generating a random permutation until a derangement is obtained. This and our procedure are both linear with respect to the number of calls to the random generator, but we obtain an improvement of more than 36%. By using...

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p