相关论文: Asymptotics for connected graphs and irreducible t…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We count cycles of an unbounded length in generalized Johnson graphs. Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length.
In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…
For a set F of finite tournaments, the F-free orientation problem is the problem of deciding if a given finite undirected graph can be oriented in such a way that the resulting oriented graph does not contain any member of F. Using the…
A sharp asymptotic formula for the number of strongly connected digraphs on $n$ labelled vertices with $m$ arcs, under a condition $m-n\to\infty$, $m=O(n)$, is obtained; this solves a problem posed by Wright back in $1977$. Our formula is a…
We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for more than half of the graphs, and very close lower and upper…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
We consider arbitrary graphs $G$ with $n$ vertices and minimum degree at least $\delta n$ where $\delta>0$ is constant. If the conductance of $G$ is sufficiently large then we obtain an asymptotic expression for the cover time $C_G$ of $G$…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
Zaremba's conjecture concerns a formation of continued fraction expansions for rational numbers with partial quotient bounded by an absolute constant. We present asymptotic estimates for the size of $\epsilon$-thickening of certain fractal…
We give a probabilistic interpretation of the coefficients of the elementary symmetric function expansion of the chromatic quasisymmetric function for any unit interval graph. As a corollary, we prove the Stanley--Stembridge conjecture.
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint…
We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and…
We prove that in a random tournament the events $\{s\rightarrow a\}$ and $\{t\rightarrow b\}$ are positively correlated, for distinct vertices $a,s,b,t \in K_n.$ It is also proven that the correlation between the events $\{s\rightarrow a\}$…
In this paper, we use a formula obtained in [8] to study certain asymptotic behaviors of GUE (Gaussian unitary ensemble) correlators. More precisely, we obtain large genus asymptotics of enumerations of ordinary graphs and ribbon graphs…
This paper investigates asymptotic estimates for the entrance probability of the discounted aggregate claim vector from a multivariate renewal risk model into some rare set. We provide asymptotic results for the entrance probability on both…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple…