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Markov property of determinantal processes with extended sine, Airy, and Bessel kernels
Determinantal processes Correlation kernels Random matrix theory Infinite particle systems Markov property Entire function and topology
2011/7/7
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initi...
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
suprema of Gaussian processes omega results random multiplicative function
2011/1/17
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic,but supply strong information when one is only ...
Concave Majorants of Random Walks and Related Poisson Processes
Concave Majorants Related Poisson Processes
2010/11/19
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providin...
On Rice's formula for stationary multivariate piecewise smooth processes
level crossings Rice’s formula stationarity Palm probabilities
2010/12/9
Let X = {Xt : t ≥ 0} be a stationary piecewise continuous Rd-valued process that moves between jumps along the integral curves of a given continuous vector field,S ⊂ Rd be a smooth surface. The ...
Empirical processes, typical sequences and coordinated actions in standard Borel spaces
Terms—Coordination via communication empirical processes Glivenko–Cantelli classes
2010/11/26
This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distr...
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
Degenerate self-similar measures spectral asymptotics small deviations of Gaussian processes
2010/12/1
The problem of small ball behavior for the norms of Gaussian processes is intensively studied
in recent years. The simplest and most explored case is that of L2-norm. Let us consider a
Gaussian proc...