Related papers: Wallach sets and squared Bessel particle systems
This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are…
We study the existence and uniqueness of SDEs describing squared Bessel particles systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties.
A multidimensional version of the Yamada-Watanabe theorem is proved. It implies a spectral matrix Yamada-Watanabe theorem. It is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared…
Necessary conditions for the existence of non-central Wishart distributions are given. Our method relies on positivity properties of spherical polynomials on Euclidean Jordan Algebras and advances an approach by Peddada and Richards (1991),…
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in…
We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using…
We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type "welcher-weg" experiment beyond the limitations set by Bohr's Principle of Complementarity. Applying classical logic, we…
We investigate the combinatorial discrepancy of geometric set systems having bounded shallow cell complexity in the \emph{Beck-Fiala} setting, where each point belongs to at most $t$ ranges. For set systems with shallow cell complexity…
We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
Following Assiotis (2020), we study general $\beta$-Hua-Pickrell diffusions of $N$ particles on $\mathbb R$ as solutions of the stochastic differential equations (SDEs) $$dX_{j,t}=\sqrt{2(1+X_{j,t}^2)}\,dB_{j,t}+\beta\left[b-a…
Motivated by problems in control theory concerning decay rates for the damped wave equation $$w_{tt}(x,t) + \gamma(x) w_t(x,t) + (-\Delta + 1)^{s/2} w(x,t) = 0,$$ we consider an analogue of the classical Paneah-Logvinenko-Sereda theorem for…
We study Bessel processes on Weyl chambers of types A and B on $\mathbb R^N$. Using elementary symmetric functions, we present several space-time-harmonic functions and thus martingales for these processes $(X_t)_{t\ge0}$ which are…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity…
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…
In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the…
We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we…