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math-ph2022
A Metric Graph for Which the Number of Possible Endpoints of a Random Walk Grows Minimally
V. L. Chernyshev, A. A. Tolchennikov
We prove that metric graph with the minimal growth of the number of possible endpoints of a random walk is the union of several linear paths coming out of the same vertex
math-ph2014★ 3 cited
How the permutation of edges of a metric graph affects the number of points moving along the edges
V. L. Chernyshev, A. A. Tolchennikov
We consider a dynamical system on a metric graph, that corresponds to a semiclassical solution of a time-dependent Schrödinger equation. We omit all details concerning mathematical…
math-ph2014★ 4 cited
Asymptotic estimate for the number of Gaussian packets on three decorated graphs
V. L. Chernyshev, A. A. Tolchennikov
We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, i.e. a decorated graph. We construct a semiclassical asymptotics of the…