Related papers: Volume growth for infinite graphs and translation …

We prove estimates relating exponential or sub-exponential volume growth of weighted graphs to the bottom of the essential spectrum for general graph Laplacians. The volume growth is computed with respect to a metric adapted to the…

We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…

We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to…

Volume entropy is an important invariant of metric graphs as well as Riemannian manifolds. In this note, we calculate the change of volume entropy when an edge is added to a metric graph. Using the first result, we investigate the change of…

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).

We give quadratic upper bounds for the asymptotic dimensions of the arc graphs and disk graphs.

We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we…

In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants,…

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…

We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs…

I compute several terms of the asymptotic expansion of the number of connected labelled graphs with n nodes and m edges, for small k=m-n.

We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…

We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial…

This paper shows certain classes of metric spaces characterized by volume growth properties of balls can viewed as graphs with infinitesimal edges. Our approach is based on nonstandard analysis.

In a previous paper Hua-Jost-Liu, we have applied Alexandrov geometry methods to study infinite semiplanar graphs with nonnegative combinatorial curvature. We proved the weak relative volume comparison and the Poincar\'e inequality on these…

We prove that the metric balls of a Hilbert geometry admit a volume growth at least polynomial of degree their dimension. We also characterise the convex polytopes as those having exactly polynomial volume growth of degree their dimension.

A few years ago various disparities for Laplacians on graphs and manifolds were discovered. The corresponding results are mostly related to volume growth in the context of unbounded geometry. Indeed, these disparities can now be resolved by…