Related papers: Statistical properties of braid groups in locally …
A Haag-Ruelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed.
We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that a given word w takes the value 1 when evaluated in G in…
This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…
A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint…
We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of…
We construct examples of localizations in the category of groups which take the Mathieu group $M_{11}$ to groups of arbitrarily large cardinality which are ``abelian up to finitely many generators''. The paper is part of a broader study on…
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of words of equal length. The sprawl quantifies a certain…
This article presents a 3-local characterisation of the sporadic simple group McL and its automorphism group. The theorem is underpinned by a further identification theorem the proof of which is character theoretic. The main theorem is…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
Garside families have recently emerged as a relevant context for extending results involving Garside monoids and groups, which themselves extend the classical theory of (generalized) braid groups. Here we establish various characterizations…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we…
This is a collection of examples showing how the GAP system can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in the…
Local convergence techniques have become a key methodology to study sparse random graphs. However, convergence of many random graph properties does not directly follow from local convergence. A notable, and important, such random graph…
The Grouped Horseshoe distribution arises from hierarchical structures in the recent Bayesian methodological literature aimed at selection of groups of regression coefficients. We isolate this distribution and study its properties…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
Measure free factors are a generalization of the notion of free factors of a group, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by…
We define a local analogue to Gromov's loop division property which is use to give a sufficient condition for an asymptotic cone of a complete geodesic metric space to have uncountable fundamental group. As well, this property is used to…