Related papers: The $S$-transform in arbitrary dimensions
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Fa\`a di Bruno algebra, and then to the group of a free operad over Schr\"oder trees. This leads to new combinatorial…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics. First we extend and unify the Kleisli category of probabilistic morphisms proposed by Lawvere and Giry…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
We adapt methods from quiver representation theory and Hall algebra techniques to the counting of representations of virtually free groups over finite fields. This gives rise to the computation of the E-polynomials of…
The paper describes some probabilistic and combinatorial aspects of the nonlinear Fourier transform associated with the AKNS-ZS problems. In the first of the two main results, we show that a family of polytopes that appear in a power…
Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the ``ordered'' and ``chaotic'' distribution of such pairs by solving the eigenvalue…
We generalize Dirichlet's $S$-unit theorem from the usual group of $S$-units of a number field $K$ to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over $S$. Specifically, we demonstrate…
A massive relativistic spinning point particle in any number of dimensions has in a previous article been shown to be described by first class constraints, which define a gauge theory. In the present paper we find the corresponding finite…
We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…
We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
A unitary transformation $\Ps [E]=\exp (i\O [E]/g) F[E]$ is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because $\o^a_i\equiv -\d\O…
The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees.
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
The target of this article is to discuss the concept of \textit{commuting probability} of finite groups which, in short, is a probabilistic measure of how abelian our group is. We shall compute the value of commuting probability for many…
We study sets of solutions to equations over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structre theory we obtain enable us to answer some questions of A. Tarski's, and…