In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...

 This paper mainly considers a nonstandard risk model with a constant interest rate‎, ‎where both the claim sizes and the inter-arrival times follow some certain dependence structures‎. ‎When the claim sizes are dominatedly varying-tailed‎, ‎asymptotics for the infinite time ruin probability of the above dependent risk model have been given‎.

this paper mainly considers a nonstandard risk model with a constant interest rate‎, ‎where both the claim sizes and the inter-arrival times follow some certain dependence structures‎. ‎when the claim sizes are dominatedly varying-tailed‎, ‎asymptotics for the infinite time ruin probability of the above dependent risk model have been given‎.

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L2 convergence of Szegő asymptotics on the spectrum.

Asymptotic properties of estimators of covariance parameters in spatial statistics are commonly considered under the frameworks of increasing domain and fixed domain asymptotics, respectively. Although inconsistency is a general conclusion under the framework of fixed domain asymptotics, it is generally believed that consistency should generally hold under the framework of increasing domain asy...

2 This paper considers the subexponential asymptotics of the stationary distributions of GI/G/1-type Markov chains in two cases: (i) the phase transition matrix in non-boundary levels is stochastic; and (ii) it is strictly substochastic. For the case (i), we present a weaker sufficient condition for the subexponential asymptotics than those given in the literature. As for the case (ii), the sub...

Contents 1 Introduction 2 The geometry of operators of Laplace and Dirac type 3 Heat trace asymptotics for closed manifolds 4 Hearing the shape of a drum 5 Heat trace asymptotics of manifolds with boundary 6 Heat trace asymptotics and index theory 7 Heat content asymptotics 8 Heat content with source terms 9 Time dependent phenomena 10 Spectral boundary conditions 11 Operators which are not of ...

We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of Bubeck, Mossel, and Rácz in order to determine the tail asymptotics of the maximum degree of the preferential attachment tree. The proof presented here is s...

If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show appli...

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.