Related papers: Spherically Symmetric Random Permutations

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…

An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.

Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials…

A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…

This note will give an enumeration of $n$-cycles in the symmetric group ${\mathcal S}_n$ by their degree (also known as their cyclic descent number) and studies similar counting problems for the conjugacy classes of $n$-cycles under the…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

It is well known that the allowed wavefunctions for an $N$-electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such system is invariant under any…

We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group…

We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric…

Let S be the group of finite permutations of the naturals 1,2,... The subject of the paper is harmonic analysis for the Gelfand pair (G,K), where G stands for the product of two copies of S while K is the diagonal subgroup in G. The…

Let $X$ be a finite partially ordered set, $R$ an associative unital ring and $\sigma$ an endomorphism of $R$. We describe some properties of the skew incidence ring $I(X,R,\sigma)$ such as invertible elements, idempotents, the Jacobson…

We consider isomorphism properties of infinite random geometric graphs defined over a variety of metrics. In previous work, it was shown that for $\mathbb{R}^n$ with the $L_{\infty}$-metric, the infinite random geometric graph is, with…

For an arbitrary finite permutation group $G$, subgroup of the symmetric group $S_\ell$, we determine the permutations involving only members of $G$ as $\ell$-patterns, i.e., avoiding all patterns in the set $S_\ell \setminus G$. The set of…

We find a formula for the number of permutations of $[n]$ that have exactly $s$ runs up and down. The formula is at once terminating, asymptotic, and exact.

We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q with non-negative integer coefficients. Setting q=1 recovers…

We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the…

The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square with coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal distance). The…

Let $F_n$ be an $n$ by $n$ symmetric matrix whose entries are bounded by $n^{\gamma}$ for some $\gamma>0$. Consider a randomly perturbed matrix $M_n=F_n+X_n$, where $X_n$ is a random symmetric matrix whose upper diagonal entries $x_{ij}$…

The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black…

The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized convolution following the idea given in [1]. The…