A ug 2 00 6 Complex determinantal processes and H 1 noise

Complex determinantal processes and H noise

For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan-tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant measure. We show that as ρ → ∞, after centering, these processes converge to invariant H 1 noise. More precisely, for all functions f ∈ H 1 (ν) ∩ L 1 (ν) the distribution of z∈Z f (z) − ρ π f dν converges to Gaussian with m...

ar X iv : m at h / 03 08 27 0 v 1 [ m at h . FA ] 2 8 A ug 2 00 3 SOME BOAS - BELLMAN TYPE INEQUALITIES IN 2 - INNER PRODUCT SPACES

Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.

m at h . A C ] 2 2 A ug 2 00 6 COMBINATORIAL SYMBOLIC POWERS SETH

Symbolic powers of ideals are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...

ar X iv : h ep - e x / 00 08 06 5 v 1 2 6 A ug 2 00 0 Search for Large Extra Dimensions in Dielectron and Diphoton Production

ar X iv : 0 70 5 . 24 60 v 1 [ m at h . PR ] 1 7 M ay 2 00 7 Noncolliding Brownian Motion and Determinantal Processes ∗

A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson’s BM model, which is a process of eigenvalues of hermitian matrixvalued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the h-transform of absorbing BM in a Weyl chamber, where the harmonic function h is the product of differences of variables (the Vande...