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Some remarks on tangent martingale difference sequences in L1-spaces
tangent martingale difference sequences L1-spaces
2009/3/31
Let X be a Banach space. Suppose that for all p in (1, ∞) a constant Cp,X depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequenc...
Dynamical properties and characterization of gradient drift diffusions
Dynamical properties gradient drift diffusions
2009/3/31
We study the dynamical properties of the Brownian diffusions having σ Id as diffusion coefficient matrix and b=∇U as drift vector. We characterize this class through the equality D+2=D-2, where ...
Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to a...
On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups
isotropic Gaussian fields homogeneous spaces compact groups
2009/3/30
Let $T$ be a random field weakly invariant under the action of a compact group $G$. We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. As a ...
A dynamical characterization of Poisson-Dirichlet distributions
dynamical characterization Poisson-Dirichlet distributions
2009/3/30
We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions PD(α,0). Precis...
Degree distribution nearby the origin of a preferential attachment graph
preferential attachment graph Degree distribution
2009/3/30
In a 2-parameter scale free model of random graphs it is shown that the asymptotic degree distribution is the same in the neighbourhood of every vertex. This degree distribution is still a power law w...
Multiplication of free random variables and the S-transform：the case of vanishing mean
free random variable S-transform vanishing mean
2009/3/27
This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right i...
Some LIL type results on the partial sums and trimmed sums with multidimensional indices
random variable strong limit theorem LIL type result
2009/3/27
Let {X, Xn; n ∈ Nd} be a field of i.i.d. random variables indexed by d-tuples of positive integers and let Sn=∑k≤nXk. We prove some strong limit theorems for Sn. Also, when d≥ 2 and h(n) satisfies som...
GRAPHICAL REPRESENTATION OF SOME DUALITY RELATIONS IN STOCHASTIC POPULATION MODELS
duality relations STOCHASTIC POPULATION MODELS particle process
2009/3/27
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. MR2123250) and for the self-duality of Feller's branching diffu...
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...
Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems
self-similar long-range dependence Gaussian processes Brownian Motion
2009/3/27
In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance ∫0min(s,t) ua [(t-u)b+(s-u)b]du,parameters a > -1, -1 < b ≤ 1, |b| ≤ 1 + a, corresp...
On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups
characterization homogeneous spaces compact groups
2009/3/23
Let $T$ be a random field weakly invariant under the action of a compact group $G$. We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. ...
A dynamical characterization of Poisson-Dirichlet distributions
dynamical characterization distributions Ruzmaikina Aizenman
2009/3/23
We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions PD(α,0). Precis...
Some LIL type results on the partial sums and trimmed sums with multidimensional indices
LIL type results partial sums trimmed sums
2009/3/23
Let {X, Xn; n ∈ Nd} be a field of i.i.d. random variables indexed by d-tuples of positive integers and let Sn=∑k≤nXk. We prove some strong limit theorems for Sn. Also, when d≥ 2 and h(n) satisfies som...
On asymptotic properties of the rank of a special random adjacency matrix
asymptotic property random matrix adjacency matrix
2009/3/23
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...