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In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n^{1/2} X_n...
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sampl...
In this paper we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, mult...
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...
Random Walk in Dynamic Markovian Random Environment.
Percolating paths through random points.
A number of papers have examined various aspects of ``random random walks'' on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss s...
Let $mu$ be a Gaussian measure on some measurable space ${W = {w}, calB (W)}$ and let $nu$ be a measure on the same space which is absolutely continuous with respect to $nu$. The paper surveys results...
The models surveyed include generalized Polya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of ...
In this note the almost sure convergence of stationary, $varphi$-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the ful...
We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with respecti...
This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable cond...
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local ``random-to-front'' reorderings, driven by a probability distribution on subsets of ...
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
Consider a two-person zero-sum game played on a random n by n matrix where the entries are iid normal random variables. Let Z be the number of rows in the support of the optimal strategy for player I ...

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