Related papers: Freely infinitely divisible $R$-diagonal elements …
Motivated by recent developments on random polymer models we propose a generalisation of reflected Brownian motion (RBM) in a polyhedral domain. This process is obtained by replacing the singular drift on the boundary by a continuous one…
In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion. We show that, under some computability conditions on these…
We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints,…
At finite $N$ the ring of gauge invariant operators is not freely generated. For problems of interest in physics, these rings are Cohen--Macaulay and admit a Hironaka decomposition, in which the full invariant ring is a free module over a…
A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…
We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We…
In the context of operator valued W*-free probability theory, we study Haar unitaries, R-diagonal elements and circular elements. Several classes of Haar unitaries are differentiated from each other. The term bipolar decomposition is used…
We introduce a new geometric-analytic functional that we analyse in the context of free discontinuity problems. Its main feature is that the geometric term (the length of the jump set) appears with negative sign. This is motivated by…
The triangular elliptic operators are natural extensions of the elliptic deformation of circular operators. We obtain a Brown measure formula for the sum of a triangular elliptic operator $g_{_{\alpha, \beta, \gamma}}$ with a random…
A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the twelve values at the three Gauss points on each of the four edges. Due to the existence of one…
The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodules and non-commutative functions techniques, we obtain analogues of…
The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of the Brownian motion on $\mathsf{GL}(N;\mathbb{C}),$ in the sense of $\ast $-distributions. The natural candidate for the large-$N$ limit of the empirical distribution…
In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two…
We define and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is $d^p$-superstable (superstable wrt. the perturbation topology), weakly simple and has complete type spaces and we…
We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index $\alpha$ and an asymmetry coefficient $\rho$. We prove that the Boolean stable law is freely infinitely divisible…
We consider the disordered monomer-dimer model on cylinder graphs $\mathcal{G}_n$, i.e., graphs given by the Cartesian product of the line graph on $n$ vertices, and a deterministic graph. The edges carry i.i.d. random weights, and the…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \mathbb{R}^{N}$ is a bounded domain, we prove new properties of solutions of \[ u_t-\Delta_p u = \mu \quad \text{in $Q$} \] with Dirichlet boundary conditions, where…
Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such…
We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the $S$-transform of an…