Related papers: Spherically Symmetric Random Permutations

We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance problem consists in investigating if the…

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The…

We prove a Central Limit Theorem for the Critical Points of Random Spherical Harmonics, in the High-Energy Limit. The result is a consequence of a deeper characterizations of the total number of critical points, which are shown to be…

The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and…

We classify spherical quadrilaterals up to isometry in the case when one inner angle is a multiple of pi while the other three are not. This is equivalent to classification of Heun's equations with real parameters and one apparent…

This paper discusses the permutations that are generated by rotating $k \times k$ blocks of squares in a union of overlapping $k \times (k+1)$ rectangles. It is found that the single-rotation parity constraints effectively determine the…

We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…

We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…

Let Sym_n denote the symmetric group of all permutations pi = a_1...a_n of {1,...,n}. An index i is a peak of pi if a_{i-1} < a_i > a_{i+1} and we let P(pi) be the set of peaks of pi. Given any set S of positive integers we define P(S;n) to…

It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…

The Mallows measure on the symmetric group $S_n$ is the probability measure such that each permutation has probability proportional to $q$ raised to the power of the number of inversions, where $q$ is a positive parameter and the number of…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.

Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…

Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\to \infty$, (a) the diameter of $G$ with respect to $S = \{g,h,g^{-1},h^{-1}\}$ is at most $O(n^2 (\log n)^c)$, and…

Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…

The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…

For $\tau\in S_3$, let $\mu_n^{\tau}$ denote the uniformly random probability measure on the set of $\tau$-avoiding permutations in $S_n$. Let $\mathbb{N}^*=\mathbb{N}\cup\{\infty\}$ with an appropriate metric and denote by…