Related papers: Wallach sets and squared Bessel particle systems

Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…

For a bivariate $P(x,y) \in \mathbb{R}[x,y]\setminus (\mathbb{R}[x] \cup \mathbb{R}[y])$, our first result shows that for all finite $A \subseteq \mathbb{R}$, $|P(A,A)|\geq \alpha|A|^{5/4}$ with $\alpha =\alpha(\mathrm{deg} P) \in…

We investigate the existence of well-behaved Beurling number systems, which are systems of Beurling generalized primes and integers which admit a power saving in the error term of both their prime and integer-counting function. Concretely,…

We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…

Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove the following two results. Assume there exists a non-zero polynomial $f(X,Y)\in K[X,Y]$, which has a non-trivial solution…

We take up the idea of Nelson's stochastic processes, the aim of which was to deduce Schr\"odinger's equation. We make two major changes here. The first one is to consider deterministic processes which are pseudo-random but which have the…

The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the…

This paper investigates conditions under which certain kinds of systems of bilinear equations have a unique structured solution. In particular, we look at when we can recover vectors $\boldsymbol{w},\boldsymbol{q}$ from observations of the…

Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are treated…

Classical polarization optics is naturally described by a two-dimensional complex Hilbert space (Jones vectors), so the tensor-product kinematics underlying bipartite nonseparability is already available classically. For statistical…

Let $X_1,\ldots,X_n$ be i.i.d.\ random points in the $d$-dimensional Euclidean space sampled according to one of the following probability densities: $$ f_{d,\beta} (x) = \text{const} \cdot (1-\|x\|^2)^{\beta}, \quad \|x\|\leq 1, \quad…

The reason for recalling this old paper is the ongoing discussion on the attempts of circumventing certain assumptions leading to the Bell theorem (Hess-Philipp, Accardi). If I correctly understand the intentions of these Authors, the idea…

We consider the system -\Delta u_j + a(x)u_j = \mu_j u_j^3 + \be\sum_{k\ne j}u_k^2u_j, u_j>0, \qquad j=1,...,n, on a possibly unbounded domain $\Om\subset\R^N$, $N\le3$, with Dirichlet boundary conditions. The system appears in nonlinear…

Consider the subset of a Weyl group with a fixed descent set. For Weyl groups of classical types, we determine the number of two-sided cells this subset intersect. Moreover, we apply this result to prove that certain rational Whittaker…

Given any closed Riemannian manifold $M$, we construct a reversible diffusion process on the space ${\mathcal P}(M)$ of probability measures on $M$ that is (i) reversible w.r.t.~the entropic measure ${\mathbb P}^\beta$ on ${\mathcal P}(M)$,…

A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at $\Delta = - \frac12$ and various symmetry classes of alternating sign matrices. Here we use the integrability of the…

We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two…

In recent experiments, localized and stationary pulses have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate with those of nondiffracting and nondispersing polychromatic Bessel…

We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case,…

We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential…