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Random Walk on a Co-Compact Fuchsian Group: Behavior of the Green's Function at the Spectral Radius
hyperbolic group surface group randomwalk Green’s function Gromov boundary Martin boundary Ruelle operator theorem
2011/9/22
Abstract: It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also show...
Abstract: A cyclic random walk is a random walk whose transition probabilities/rates can be written as a superposition of the empirical measures of a family of finite cycles. This identifies a convex ...
Positivity of integrated random walks
Integrated random walk persistence one-sided exit probability unilateral small deviations area of random walk
2011/9/20
Abstract: Take a centered random walk S_n and consider the sequence of its partial sums A_n = S_1 + ... + S_n. Suppose S_1 is in the domain of normal attraction of an alpha-stable law with 1 < \alpha ...
Distance Functions, Critical Points, and Topology for Some Random Complexes
Distance function critical points Morse index Cech complex Poisson process central limit theorem Betti numbers
2011/9/20
Abstract: For a finite set of points $P$ in $R^d$, the function $d_P:R^d \to R_+$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is random. In par...
The Size of the Largest Part of Random Weighted Partitions of Large Integers
Random Weighted Partitions Large Integers Probability
2011/9/20
Abstract: For a given sequence of weights (non-negative numbers), we consider partitions of the positive integer n. Each n-partition is selected uniformly at random from the set of all such partitions...
Characterizations of distributions via order statistics with random exponential shifts
characterizations order statistics exponential distribution generalized logistic distribution
2011/9/19
Abstract: A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile fu...
Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables
Explicit Bounds Dependent Normally Distributed Random Variables Distribution Function of the Sum
2011/9/19
Abstract: In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the i...
Stochastic Service Systems, Random Interval Graphs and Search Algorithms
Queueing theory interval graphs Lambert series asymptotic expansions
2011/9/15
Abstract: We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorith...
Tail estimates for norms of sums of log-concave random vectors
log-concave random vectors concentration inequalities deviation inequalities random matrices
2011/9/15
Abstract: We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the nor...
Free Completely Random Measures
Bayesian non parametrics Bercovici-Pata bijection free completely random measures free infinite divisibility free probability
2011/9/15
Abstract: Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An importa...
Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian Processes
tail asymptotic Laplace method self-similar processes Gaussian processes locally stationary processes
2011/9/15
Abstract: We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome bu...
Universality of Correlations for Random Analytic Functions
Universality of Correlations Random Analytic Functions Probability
2011/9/16
Abstract: We review a result obtained with Andrew Ledoan and Marco Merkli. Consider a random analytic function $f(z) = \sum_{n=0}^{\infty} a_n X_n z^n$, where the $X_n$'s are i.i.d., complex valued ra...
Record process on the Continuum Random Tree
continuum random tree, records, cutting down a tree
2011/9/14
Abstract: We consider the number of cuts $X_n^*$ needed to isolate the root of the sub-tree spanned by $n$ leaves uniformly chosen at random in Aldous's continuum random tree $\ct$. We prove the almos...
On possible mixing rates for some strong mixing conditions for N-tuplewise independent random fields
Random field mixing conditions mixing rates N-tuplewise independence
2011/9/15
Abstract: For a given pair of positive integers $d$ and $N$ with $N \geq 2$, for strictly stationary random fields that are indexed by the $d$-dimensional integer lattice and satisfy $N$-tuplewise ind...
Moderate Deviation Principle for dynamical systems with small random perturbation
Freidlin-Wentzell’s theorem large deviations moderate deviations Talagrand’s transportation inequality
2011/9/14
Abstract: Consider the stochastic differential equation in $\rr^d$
dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t
X^{\e}_0&=x_0,\quad x_0\in\rr^d
where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...