We analyse the tail behaviour of stationary response times in the class of open stochastic networks with renewal input admitting a representation as (max; +){linear systems. For a K-station tandem network of single server queues with innnite buuer capacity, which is one of the simplest models in this class, we rst show that if the tail of the service time distribution of one server, say server ...

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L2 norm. 1. Results Let μ be a nite positive Borel measure on [−1, 1] and let {pn}n=0 denote the corresponding orthonormal polynomials, so that ∫...

We calculate the main asymptotic terms for eigenvalues, both simple and multiple, and eigenfunctions of the Neumann Laplacian in a three-dimensional domain Ω(h) perturbed by a small (with diameter O(h)) Lipschitz cavern ωh in a smooth boundary ∂Ω = ∂Ω(0). The case of the hole ωh inside the domain but very close to the boundary ∂Ω is under consideration as well. It is proven that the main correc...

New limit theory is developed for co-moving systems with explosive processes, connecting continuous and discrete time formulations. The theory uses double asymptotics with infill (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provided for single and multiple explosive regressor...

In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and ...

We derive in this paper the asymptotics of several-partition Hurwitz numbers, relying on a theorem of Kazarian for the one-partition case and on an induction carried on by Zvonkine. Essentially, the asymptotics for several partitions is the same as the one-partition asymptotics obtained by concatenating the partitions. Résumé. Dans cet article, nous donnons l’asymptotique générale des nombres d...

Then qk(t) = log det (I +Kk)− log det (I +Kk−1) is a solution to the system of equations. If ρ is supported in the set of nth roots of unity then the solution is n-periodic in that qk+n = qk for all k. The main interest is in the limit t→ 0+, while the t→ ∞ asymptotics are straightforward. The asymptotics for the qk are known once those for the determinants are, and since ρ is arbitrary there i...

The one-dimensional Schrödinger equation is considered when the potential is real valued, integrable, and has a finite first moment. The small-energy asymptotics of the logarithmic spatial derivative of the Jost solutions are established. Some consequences of these asymptotics are presented such as the small-energy limits of the scattering coefficients and a simplified characterization of the s...

We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer’s sojourn time in two regimes: the customer arrives in an empty system, and the customer arrives in the system in the stationary regime. In particular, in the case of Poisson input we use the branching pro...

Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal pol...