Related papers: Hypercontractivity on High Dimensional Expanders: …
Hypercontractivity is one of the most powerful tools in Boolean function analysis. Originally studied over the discrete hypercube, recent years have seen increasing interest in extensions to settings like the $p$-biased cube, slice, or…
The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly…
We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). Let $X$ be a $k$-dimensional HDX. We show for any $i\leq k$ and $f:X(i)\to [0,1]$: \[\Pr_{s\in X(k)}\left[\left|\underset{{t\subseteq…
The classical hypercontractive inequality for the noise operator on the discrete cube plays a crucial role in many of the fundamental results in the Analysis of Boolean functions, such as the KKL (Kahn-Kalai-Linial) theorem, Friedgut's…
The hypercontractive inequality on the discrete cube plays a crucial role in many fundamental results in the Analysis of Boolean functions, such as the KKL theorem, Friedgut's junta theorem and the invariance principle. In these results the…
We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…
Bourgain's symmetrization theorem is a powerful technique reducing boolean analysis on product spaces to the cube. It states that for any product $\Omega_i^{\otimes d}$, function $f: \Omega_i^{\otimes d} \to \mathbb{R}$, and $q > 1$:…
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely…
For a function $f$ on the hypercube $\{0,1\}^n$ with Fourier expansion $f=\sum_{S\subseteq[n]}\hat f(S)\chi_S$, the hypercontractive inequality allows bounding norms of $T_\rho f=\sum_S\rho^{|S|} \hat f(S)\chi_S$ in terms of norms of $f$.…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over…
We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hypercontractive, whenever it is restricted to non-increasing mappings on configuration spaces. We deduce from this result some versions of…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
We propose a new tool, which we call $M$-decompositions, for devising superconvergent hybridizable discontinuous Galerkin (HDG) methods and hybridized-mixed methods for linear elasticity with strongly symmetric approximate stresses on…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…
In this work we develop a weight theory in the setting of hyperbolic spaces. Our starting point is a variant of the well-known endpoint Fefferman-Stein inequality for the centered Hardy-Littlewood maximal function. This inequality…
Small set expansion in high dimensional expanders is of great importance, e.g., towards proving cosystolic expansion, local testability of codes and constructions of good quantum codes. In this work we improve upon the state of the art…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple…
We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foias characteristic functions of contractions. We present an explicit method…