Related papers: Hypercontractive measures, Talagrand's inequality,…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…
Talagrand's inequality for independent Bernoulli random variables is extended to many interacting particle systems (IPS). The main assumption is that the IPS satisfies a log-Sobolev inequality. In this context it is also shown that a…
We reveal a connection of the Brascamp-Lieb inequality with Skorokhod embedding. Error bounds for the inequality in terms of variance are also provided.
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
We study two dimensional $\mathcal{N} = (2, 2)$ Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large $N$ techniques. We…
We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application we show concentration results for the…
We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse…
We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…
We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological…
We investigate in a systematic way hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non homogeneous diffusions in $\mathbb{R}^{n}$. We provide an explicit construction of a family of Orlicz…
We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic…
Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Brinkman's or Darcy's). While each of these models has been…
We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products.…
We continue the $U$-bound program initiated in [J. Funct. Anal. 258, 814-851 (2010)] and prove super-Poincar\'e inequalities for a class of subelliptic probability measures defined on M\'etivier groups, the main ingredient in the proof…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects.…
We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…
In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity…
In this paper we develop a measure-theoretic method to treat problems in hypergraph theory. Our central theorem is a correspondence principle between three objects: An increasing hypergraph sequence, a measurable set in an ultraproduct…
We show that liquids and certain holographic models are strikingly similar in terms of several detailed and specific properties related to their energy spectra. We consider two different holographic models and ascertain their similarity…