Related papers: Concentration of Haar measures, with an applicatio…
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…
We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another…
We introduce and investigate in this short report the new notion of uniform measure (distribution) on the arbitrary compact metric space. We consider also some possible applications of these measures in the theory of imbedding theorems and…
We consider two $n\times n$ non-Hermitian random matrices such that the $ij$th entry of one matrix is correlated with the $ij$th entry of the other matrix. However, the entries of any particular matrix are i.i.d. random variables. We study…
The main result of this paper states that for independent random variables $X, Y$ taking values in a compact metrisable abelian group, $X + Y$ has the same distribution as $X$, if and only if there exists a compact subgroup $A$ such that…
In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H}_{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
In this paper, we will study the behavior of the space of positive harmonic functions associated with the random walk on a discrete group under the change of probability measure by a randomized stopping time. We show that this space remains…
The complete representation of the Martin compactification for reflected random walks on a half-space $\Z^d\times\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial''…
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to…
Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive…
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…
We consider a set of probability measures on a finite event space $\Omega$. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
We prove that a sum of random matrices generated by a $\psi$-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp…
In this paper we present a new criterion to determine when the normalized Haar measure on a compact topological group is a Pietsch measure for nonlinear summing mappings. As a consequence, we provide a partial answer to a problem raised by…
Certain previously known upper bounds on the moments of the norm of martingales in 2-smooth Banach spaces are improved. Some of these improvements hold even for sums of independent real-valued random variables. Applications to concentration…