284 research outputs found
Zero distribution of polynomials satisfying a differential-difference equation
In this paper we investigate the asymptotic distribution of the zeros of
polynomials satisfying a first order differential-difference
equation. We give several examples of orthogonal and non-orthogonal families.Comment: 26 pages, 2 figure
An algebraic approach to Polya processes
P\'olya processes are natural generalization of P\'olya-Eggenberger urn
models. This article presents a new approach of their asymptotic behaviour {\it
via} moments, based on the spectral decomposition of a suitable finite
difference operator on polynomial functions. Especially, it provides new
results for {\it large} processes (a P\'olya process is called {\it small} when
1 is simple eigenvalue of its replacement matrix and when any other eigenvalue
has a real part ; otherwise, it is called large)
Limit theorems for numbers satisfying a class of triangular arrays
The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian
Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
The statistical properties of quantum transport through a chaotic cavity are
encoded in the traces \T={\rm Tr}(tt^\dag)^n, where is the transmission
matrix. Within the Random Matrix Theory approach, these traces are random
variables whose probability distribution depends on the symmetries of the
system. For the case of broken time-reversal symmetry, we present explicit
closed expressions for the average value and for the variance of \T for all
. In particular, this provides the charge cumulants \Q of all orders. We
also compute the moments of the conductance . All the
results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of
open channels.Comment: 5 pages, 4 figures. v2-minor change
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