相关论文: Products of free random variables and k-divisible …

We study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicity--free discrete direct sum of irreducible representations. Then we look at…

In a random model of minimum cost bipartite matching based on exponentially distributed edge costs, we show that the distribution of the cost of the optimal solution can be computed efficiently. The distribution is represented by its moment…

Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…

We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

To find moments of various estimators related to Autoregressive models of Statistics, one first needs the cumulants of products of two Normally distributed random variables. The purpose of this article is to derive the corresponding…

The asymptotic study of tuples of random non-increasing integers is crucial for probabilistic models coming from asymptotic representation theory and statistical physics. We study the global behavior of such tuples, introducing a new family…

We give a criterion for the Kac conjecture asserting that the free term of the polynomial counting the absolutely indecomposable representations of a quiver over a finite field of given dimension coincides with the corresponding root…

We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions…

The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating $k$-independent random values over a…

We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…

Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…

The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity,…

Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…

In this paper, we study the partial bi-free $S$-transform of a pair $(a,b)$ of random variables, and the $S$-transform of the $2\times 2$ matrix-valued random variable $\left(\begin{matrix}a&0\\0&b\end{matrix}\right)$ associated with…

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…

We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the n-th moment <Z^n> of the partition function is given by the ground state energy…

We show that the sum of two free random variables can have a free Poisson law without any of them having a free Poisson law.

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…