Related papers: Statistical properties of braid groups in locally …
Many loads have flexibility in demand that can be used to provide ancillary services to power grids. A large body of literature exists on designing algorithms to coordinate actions of many loads to provide such a service. The topic of…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we…
We define specific multiplicities on the braid arrangement by using edge-bicolored graphs. To consider their freeness, we introduce the notion of bicolor-eliminable graphs as a generalization of Stanley's classification theory of free…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
In this work the author studies the property close to property of order separability.
The paper contains enumerative combinatorics for positive braids, square free braids, and simple braids, emphasizing connections with classical Fibonacci sequence. The simple subgraph of the Cayley graph of the braid group is analyzed in…
We show that if one selects uniformly independently and identically distributed matrices $A_1, \ldots, A_s \in \mathrm{SL}_2(\mathbb{Z})$ from a ball of large radius $X$ then with probability at least $1 - X^{-1 + o(1)}$ the matrices $A_1,…
We explore a natural extension of braid arrangements in the context of determinantal arrangements. We show that these determinantal arrangements are free divisors. Additionally, we prove that free determinantal arrangements defined by the…
In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach.…
Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…
This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite $p$-groups with the smallest maximum size for neighborhoods of…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
We introduce a new model of random Artin groups. The two variables we consider are the rank of the Artin groups and the set of permitted coefficients of their defining graphs. The heart of our model is to control the speed at which we make…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
To any free group automorphism, we associate a real pretree with several nice properties. First, it has a rigid/non-nesting action of the free group with trivial arc stabilizers. Secondly, there is an expanding pretree-automorphism of the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
In [V.O. Manturov, Non-reidemeister knot theory and its applications in dynamical systems, geometry, and topology, arxiv:1501.05208] the first named author gave the definition of $k$-free braid groups $G_n^k$. Here we establish connections…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…