Related papers: Statistical properties of braid groups in locally …
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…
Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
When modeling a social dynamics with an agent-oriented approach, researchers have to describe the structure of interactions within the population. Given the intractability of extensive network collecting, they rely on random network…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of…
An approach to modelling random sets with locally finite perimeter as random elements in the corresponding subspace of $L^1$ functions is suggested. A Crofton formula for flat sections of the perimeter is shown. Finally, random processes of…
NOTE: PAPER WITHDRAWN (See Comments) The Clifford and Local Clifford groups for $d > 2$ dimensional systems have been topics of recent interest due to their applications in graph states, quantum codes, and possible applications in fast…
We compare two crossed homomorphisms on a braid group, one defined diagrammatically and the other defined algebraically. We show that these crossed homomorphisms are essentially the same, and compute them in detail for simple braids, namely…
We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the…
The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K $\ge$ 2 independent copies of X. We provide a constructive estimator based on a suitable definition of…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in…
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…
Log-linear models are often used to estimate the size of a closed population using capture-recapture data. When capture probabilities are related to auxiliary covariates, one may select a separate model based on each of several post-strata.…
I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii)…
We provide new group presentations for surface braid groups which are positive. We study some properties of such presentations and we solve the conjugacy problem in a particular case.
Braids can be represented geometrically as curve diagrams. The geometric complexity of a braid is the minimal complexity of a curve diagram representing it. We introduce and study the corresponding notion of geometric generating function.…