37 research outputs found
Universal microscopic correlation functions for products of independent Ginibre matrices
We consider the product of n complex non-Hermitian, independent random
matrices, each of size NxN with independent identically distributed Gaussian
entries (Ginibre matrices). The joint probability distribution of the complex
eigenvalues of the product matrix is found to be given by a determinantal point
process as in the case of a single Ginibre matrix, but with a more complicated
weight given by a Meijer G-function depending on n. Using the method of
orthogonal polynomials we compute all eigenvalue density correlation functions
exactly for finite N and fixed n. They are given by the determinant of the
corresponding kernel which we construct explicitly. In the large-N limit at
fixed n we first determine the microscopic correlation functions in the bulk
and at the edge of the spectrum. After unfolding they are identical to that of
the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic
correlations we find at the origin differ for each n>1 and generalise the known
Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde
Stein's method on Wiener chaos
We combine Malliavin calculus with Stein's method, in order to derive
explicit bounds in the Gaussian and Gamma approximations of random variables in
a fixed Wiener chaos of a general Gaussian process. We also prove results
concerning random variables admitting a possibly infinite Wiener chaotic
decomposition. Our approach generalizes, refines and unifies the central and
non-central limit theorems for multiple Wiener-It\^o integrals recently proved
(in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre,
Peccati and Tudor. We apply our techniques to prove Berry-Ess\'een bounds in
the Breuer-Major CLT for subordinated functionals of fractional Brownian
motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck
semigroups, we also recover a technical result recently proved by Chatterjee,
concerning the Gaussian approximation of functionals of finite-dimensional
Gaussian vectors.Comment: 39 pages; Two sections added; To appear in PTR
The Time Structure of Hadronic Showers in highly granular Calorimeters with Tungsten and Steel Absorbers
The intrinsic time structure of hadronic showers influences the timing
capability and the required integration time of hadronic calorimeters in
particle physics experiments, and depends on the active medium and on the
absorber of the calorimeter. With the CALICE T3B experiment, a setup of 15
small plastic scintillator tiles read out with Silicon Photomultipliers, the
time structure of showers is measured on a statistical basis with high spatial
and temporal resolution in sampling calorimeters with tungsten and steel
absorbers. The results are compared to GEANT4 (version 9.4 patch 03)
simulations with different hadronic physics models. These comparisons
demonstrate the importance of using high precision treatment of low-energy
neutrons for tungsten absorbers, while an overall good agreement between data
and simulations for all considered models is observed for steel.Comment: 24 pages including author list, 9 figures, published in JINS
On the Largest and the Smallest Singular Value of Sparse Rectangular Random Matrices
We derive estimates for the largest and smallest singular values of sparse
rectangular random matrices, assuming . We consider a model with sparsity parameter such that
for some , and assume that the moments of
the matrix elements satisfy the condition . We assume also that the entries of matrices we consider are
truncated at the level with
.Comment: arXiv admin note: text overlap with arXiv:0802.3956 by other author