ar X iv : m at h - ph / 0 51 00 12 v 1 3 O ct 2 00 5 ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE KOOSIS THEOREM

ar X iv : m at h - ph / 0 70 30 43 v 3 2 8 O ct 2 00 7 RANDOM MATRICES , NON - BACKTRACKING WALKS , AND ORTHOGONAL POLYNOMIALS

Several well-known results from the random matrix theory, such as Wigner’s law and the Marchenko–Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a rôle in this approach.

ar X iv : m at h - ph / 0 51 00 96 v 1 3 1 O ct 2 00 5 The Ehrenfest system and the rest point spectrum for a Hartree - type Equation

Following Ehrenfest's approach, the problem of quantum-classical correspondence can be treated in the class of trajectory-coherent functions that approximate as → 0 a quantum-mechanical state. This idea leads to a family of systems of ordinary differential equations, called Ehrenfest M-systems (M = 0, 1, 2,. . .), formally equivalent to the semiclassical approximation for the linear Schrödinger...

ar X iv : m at h - ph / 0 11 00 12 v 1 9 O ct 2 00 1 Functional Equations and Poincare Invariant Mechanical Systems

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincaré algebra:

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - t h / 00 10 13 6 v 1 1 7 O ct 2 00 0 HEAT TRACE ASYMPTOTICS OF A TIME DEPENDENT PROCESS

We study the heat trace asymptotics defined by a time dependent family of operators of Laplace type which naturally appears for time dependent metrics. MSC number: 58G25, 35P05.