Related papers: Weighted prime geodesic theorems
We present a quantitative version of Guessing Geodesics, which is a well-known theorem that provides a set of conditions to prove hyperbolicity of a given metric space. This version adds to the existing result by determining an explicit…
In this paper, we study sequences of perfect t-embeddings of a uniformly weighted family of graphs we call generalized tower graphs. We show that the embeddings of these graphs satisfy certain technical assumptions, in particular, the…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomass\'e, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been…
We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira…
We enumerate weighted graphs with a certain upper bound condition. We also compute the generating function of the numbers of these graphs, and prove that it is a rational function. In particular, we show that if the given graph is a…
Let $m\geq 3$. Suppose that $$ 1-2^{-2^{m^24^m}}<\gamma<1. $$ Then the set $$ \{p\text{ prime}:\, p=[n^{\frac1\gamma}]\text{ for some }n\in{\mathbb N}\} $$ contains infinitely many non-trivial $m$-term arithmetic progressions.
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
We apply a theorem of Wick to rewrite certain classes of exponential measures on random graphs as integrals of Feynman-Gibbs type, on the real line. The analytic properties of these measures can then be studied in terms of phase…
Let I=I(D) be the edge ideal of a weighted oriented graph D. We determine the irredundant irreducible decomposition of I. Also, we characterize the associated primes and the unmixed property of I. Furthermore, we give a combinatorial…
Let $\mathcal{D}$ be a weighted oriented graph and $I(\mathcal{D})$ be its edge ideal. In this paper, we investigate the Betti numbers of $I(\mathcal{D})$ via upper-Koszul simplicial complexes, Betti splittings and the mapping cone…
In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…
Given an infinite connected graph, a way to randomly perturb its metric is to assign random i.i.d. lengths to the edges of the graph. Assume that the graph is infinite and of bounded degree. Assume also strict positivity and finite…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
We find families of prime knot diagrams with arbitrary extreme coefficients in their Jones polynomials. Some graph theory is presented in connection with this problem, generalizing ideas by Yongju Bae and Morton and giving a positive answer…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.