Related papers: A von Neumann theorem for uniformly distributed se…

We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.

We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.

The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.

We show that the number of partitions of n with alternating sum k such that the multiplicity of each part is bounded by 2m+1 equals the number of partitions of n with k odd parts such that the multiplicity of each even part is bounded by m.…

Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…

We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…

The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.

We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…

The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice…

We prove a noncommutative $(p,p)$-Poincar\'e inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our…

In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smallest one. We find formulas relating to the smallest parts of…

This paper proves a convergence theorem for the push-forward Wiener measures on holonomy groups via stochastic parallel transports along convergent metric connections.

A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

We give an extension of a criterion of van der Corput on uniform distribution of sequences. Namely, we prove that a sequence $x_n$ is uniformly distributed modulo 1 if it is weakly monotonic and satisfies the conditions $\Delta^2x_n\to…

Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…

We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

Consider $d$ commuting $C_{0}$-semigroups (or equivalently: $d$-parameter $C_{0}$-semigroups) over a Hilbert space for $d \in \mathbb{N}$. In the literature (\textit{cf.} [29, 26, 27, 23, 18, 25]), conditions are provided to classify the…

We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in…

Let $S_n$ be the symmetric group, and let $Y$ be a Young subgroup of $S_n$. Let $\Pi_n$ be the complex of partitions of $\{1, \ldots, n\}$. Our main result is a $Y$-equivariant decomposition of $\Pi_n$. As an application, we obtain new…