Related papers: Coassociativity breaking and oriented graphs
In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…
We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy…
In this paper, We develop the stratified de Rham theory on singular spaces using modern tools including derived geometry and stratified structures. This work unifies and extends the de Rham theory, Hodge theory, and deformation theory of…
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…