In [17] we discussed density expansions for multidimensional diffusions ( X, . . . , X ) , at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace the well-known ”not-in-cutlocus” condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility...

Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455 Abstract: In these lectures, I shall discuss small x physics and the consequences of the high gluon density which arises as x decreases. I argue that an understanding of this problem would lead to knowledge of the high energy asymptotics of hadronic processes. The high gluon density should allow a first principles com...

In this paper, we focus on simple exponential approximations for steady-state tail probabilities in G/GI/1 queues based on large-time asymptotics. We relate the large-time asymptotics for the steady-state waiting time, sojourn time and workload. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical...

For general Riemannian foliations, spectral asymptotics of the Laplacian is studied when the metric on the ambient manifold is blown up in directions normal to the leaves (adiabatic limit). The number of “small” eigenvalues is given in terms of the differentiable spectral sequence of the foliation. The asymptotics of the corresponding eigenforms also leads to a Hodge theoretic description of th...

We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an ≡ 1, bn = −Cn−β (0 < β < 2 3 ), one has dμ(x) = w(x) dx on (−2, 2), and near x = 2, w(x) = e where Q(x) = βC 1 β Γ(32 )Γ( 1 β − 1 2 )(2 − x) 1 2 − 1 β Γ( 1 β + 1) (1 +O((2 − x)))

In this paper we obtain an estimate for the Thomas{Fermi density which plays a role in the analysis of the atomic energy asymptotics. Such estimate has obvious number{theoretic features related to the radial symmetry of a certain Schrr odinger operator, and we use number{theoretic methods in our proof. From the technical viewpoint, we also simplify and improve some of the original estimates in ...

Our talk at Lisbon SAMP conference was based mainly on our recent results on small diameter asymptotics for solutions of the Helmgoltz equation in networks of thin fibers. These results were published in [21]. The present paper contains a detailed review of [21] under some assumptions which make the results much more transparent. It also contains several new theorems on the structure of the spe...