Related papers: Hypergroups and distance distributions of random w…
Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of graphs. In this article, we reveal that his method is applicable to a random walk on a certain kind of infinite graphs.…
A pointed graph $(\Gamma,v_0)$ induces a family of transition matrices in Wildberger's construction of a hermitian hypergroup via a random walk on $\Gamma$ starting from $v_0$. We will give a necessary condition for producing a hermitian…
Wildberger has introduced the method to construct a hermitian discrete hypergroup from a random walk on a graph. We will apply his method to an open quantum random walk (OQRW) on a distance set, and show that any discrete hypergroup which…
Initial steps are presented towards understanding which finitely generated groups are almost surely generated as semigroups by the path of a random walk on the group.
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevance is how to leverage information carried in hypergraph…
We find explicit eigenvectors for the transition matrix of a random walk due to Bidegare, Hanlon and Rockmore. This is accomplished by using Brown and Diaconis' analysis of its stationary distribution, together with some combinatorics of…
A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their…
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is…
The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs. Our results…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
Hypergraphs provide a fundamental framework for representing complex systems involving interactions among three or more entities. As empirical hypergraphs grow in size, characterizing their structural properties becomes increasingly…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…