Related papers: Intertwinings and Generalized Brascamp-Lieb Inequa…
We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include…
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining…
The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of…
Dispersion effects induce new instabilities and dynamics in the weakly nonlinear description of light propagation in fiber Bragg gratings. A new family of dispersive localized pulses that propagate with the group velocity is numerically…
Based on coupling in two steps and the regularization approximations of the underlying subordinators, we establish log-Harnack inequalities for Markov semigroups generated by a class of non-local Gruschin type operators. Some concrete…
In a previous paper the authors develop an intersection theory for subspaces of rational functions on an algebraic variety X over complex numbers. In this note, we first extend this intersection theory to an arbitrary algebraically closed…
We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.
We develop the theory of the intertwining distributional versions of the LS-category and the sequential topological complexities of a space $X$, denoted by $\mathsf{icat}(X)$ and $\mathsf{iTC}_m(X)$, respectively. We prove that they satisfy…
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
In this paper, we formulate and prove a local intertwining relation for metaplectic groups assuming the local intertwining relation for non-quasi-split odd special orthogonal groups.
This paper presents some numerical simulations of the full one-dimensional Maxwell-Lorentz equations that describe light propagation in fiber Bragg gratings in order to confirm that the standard nonlinear coupled mode equations fail to…
By employing the recently obtained sharp stability versions of the Pr\'ekopa--Leindler inequality, we are able to obtain a sharp quantitative stability version for the Brascamp--Lieb inequality, as well as several different results on the…
In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations.…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack…
We study Birkhoff sums as distributions. We obtain regularity results on such distributions for various dynamical systems with hyperbolicity, as hyperbolic linear maps on the torus and piecewise expanding maps on the interval. We also give…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…