Related papers: Multidimensional Free Poisson Limits on Free Stoch…
We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Amp\`ere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we…
Let $SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices and set $SM(\mathbb{R})^g = \cup_n SM_n(\mathbb{R})^g$. A free quadrilateral is the collection of tuples $X \in SM(\mathbb{R})^2$ which have positive…
We introduce a notion of non-commutative joint independence for multiple algebras in a non-commutative probability space. The pairwise relationships between these algebras are encoded by a graph with two edge sets -- a combinatorial…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove that geometric distribution minimises R\'enyi entropy of order infinity under fixed variance, among all discrete log-concave random variables…
We show that the sum of two free random variables can have a free Poisson law without any of them having a free Poisson law.
We establish necessary and sufficient conditions implying that the product of $m\geq 2$ Poisson functionals, living in a finite sum of Wiener chaoses, is square-integrable. Our conditions are expressed in terms of iterated add-one cost…
We prove the Freiheitssatz for the variety of generic Poisson algebras.
If f is a polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes…
Let $X$ be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We show that $$ \mathbf{E}\|X\|_{S_p} \asymp \mathbf{E}\Bigg[ \Bigg(\sum_i\Bigg(\sum_j X_{ij}^2\Bigg)^{p/2}\Bigg)^{1/p} \Bigg]…
We study the asymptotic behavior of the maximum interpoint distance of random points in a $d$-dimensional set with a unique diameter and a smooth boundary at the poles. Instead of investigating only a fixed number of $n$ points as $n$ tends…
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional…
We construct two new one-parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss type formulas geared for points of any given homogeneity…
The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only…
We study unimodality for free multiplicative convolution with free normal distributions $\{\lambda_t\}_{t>0}$ on the unit circle. We give four results on unimodality for $\mu\boxtimes\lambda_t$: (1) if $\mu$ is a symmetric unimodal…
In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…
The superradiance phenomena of massive bosons and fermions in the Kerr spacetime are studied in the Bargmann-Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one…
We study fibers of word maps in finite, profinite, and residually finite groups. Our main result is that, for any word w in the free group on d generators, there exists $\epsilon > 0$ such that if G is a residually finite group with…
The universality for the local spiked eigenvalues is a powerful tool to deal with the problems of the asymptotic law for the bulks of spiked eigenvalues of high-dimensional generalized Fisher matrices. In this paper, we focus on a more…
The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the…