Related papers: Statistical properties of braid groups in locally …
Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well.…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
The density of a subgroupoid with respect to a free groupoid is defined as the asymptotic ratio of their growths. This notion can be interpreted as a generalisation of the index's inverse for groups or as the probability of an element…
We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…
In several scale free graph models the asymptotic degree distribution and the characteristic exponent change when only a smaller set of vertices is considered. Looking at the common properties of these models, we present sufficient…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories…
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded…
This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The…
Consider the braid group $B_3=< a,b| aba=bab>$ and the nearest neighbor random walk defined by a probability $\nu$ with support $\{a,a^{-1},b,b^{-1}\}$. The rate of escape of the walk is explicitly expressed in function of the unique…
We consider random walks on locally compact groups, extending the geometric criteria for the identification of their Poisson boundary previously known for discrete groups. First, we prove a version of the Shannon-McMillan-Breiman theorem,…
In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…
We introduce a notion of "freely braided element" for simply laced Coxeter groups. We show that an arbitrary group element $w$ has at most $2^{N(w)}$ commutation classes of reduced expressions, where $N(w)$ is a certain statistic defined in…
We introduce a heuristic prediction for the distribution of the isomorphism class of the Galois group of the maximal pro-p extension of Q unramified outside a "random" set of primes. This is guided by reasoning similar to that governing the…
We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids…
This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of…