Related papers: $q$-deformed Perelomov-Popov measures and quantize…
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…
Let $\Gamma\subset \bar{\mathbb Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $\alpha_1,\ldots,\alpha_r\in\bar{\mathbb Q}^\times$ be algebraic numbers which are $\mathbb{Q}$-linearly independent and let…
We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…
We study asymptotics of representations of the unitary groups U(n) in the limit as n tends to infinity and we show that in many aspects they behave like large random matrices. In particular, we prove that the highest weight of a random…
After studying some properties of the generalized exponential and logarithmic function, in particular investigating the domain where the first maintains itself real and positive, and outlining how the known dualities $q \leftrightarrow…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises naturally from representation theory, and in…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…
The metrical theory of the product of consecutive partial quotients is associated with the uniform Diophantine approximation, specifically to the improvements to Dirichlet's theorem. Achieving some variant forms of metrical theory in…
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
Let $\mathcal{M}$ be the set of Borel probability measures on $\mathbb{R}$. We denote by $\mu^{\mathrm{ac}}$ the absolutely continuous part of $\mu\in\mathcal{M}$. The purpose of this paper is to investigate the supports and regularity for…
The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$,…
We consider some general facts concerning convergence P_{n}-Q_{n}\to 0 as n\to \infty, where P_{n} and Q_{n} are probability measures in a complete separable metric space. The main point is that the sequences {P_{n}} and {Q_{n}} are not…
We study the usual stochastic order between probability measures on preordered topological abelian groups, focusing on asymptotic and catalytic versions of the order. In the asymptotic version, a measure $\mu$ dominates a measure $\nu$ if…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measures such as Bernoulli convolutions as special cases. Our main…
We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to…
We introduce a probability distribution Q on the group of permutations of the set Z of integers. Distribution Q is a natural extension of the Mallows distribution on the finite symmetric group. A one-sided infinite counterpart of Q,…