Related papers: Boolean functions with small second order influenc…

This note is concerned with an extension, at second order, of an inequality on the discrete cube $C_n=\{-1,1\}$ (equipped with the uniform measure) due to Talagrand (\cite{TalL1L2}). As an application, the main result of this note is a…

In a discrete form of the second quantization, the gauge independencies of all the physical states including vacuum in QED are restudied through a new approach. We also discuss an interesting phenomenon attributed to vacuum effect and come…

In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new…

Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…

In this note we consider Boolean functions defined on the discrete cube equipped with a biased product probability measure. We prove that if the spectrum of such a function is concentrated on the first two Fourier levels, then the function…

We introduce a new notion of influence for symmetric convex sets over Gaussian space, which we term "convex influence". We show that this new notion of influence shares many of the familiar properties of influences of variables for monotone…

Account of a system may depend on available methods of gaining information. We discuss a simple discrete system whose description is affected by a specific model of measurement and transformations. It is shown that the limited means of…

We consider various definitions of degrees of discrete functions and establish relations between the number of relevant (essential) variables and degrees of two- and three-valued functions. Keywords: relevant variable, sensitivity, degree…

Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…

In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…

We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the…

We review higher order tangent spaces and influence functions and their use to construct minimax efficient estimators for parameters in high-dimensional semiparametric models.

Keller and Kindler recently established a quantitative version of the famous Benjamini~--Kalai--Schramm Theorem on noise sensitivity of Boolean functions. The result was extended to the continuous Gaussian setting by Keller, Mossel and Sen…

We show that on every product probability space, Boolean functions with small total influences are essentially the ones that are almost measurable with respect to certain natural sub-sigma algebras. This theorem in particular describes the…

We extend our approach based on the second order perturbation theory in the Coulomb interaction recently developed for quantum dots coupled to superconducting leads to the superconducting double quantum dot setups. Using our perturbative…

We present a covariant and gauge invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor…

We prove the existence of secondary terms of order X^{5/6} in the Davenport-Heilbronn theorems on cubic fields and 3-torsion in class groups of quadratic fields. For cubic fields this confirms a conjecture of Datskovsky-Wright and Roberts.…

The entropy/influence conjecture, raised by Friedgut and Kalai in 1996, seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is…

In a recent paper, T. Austin has proved an analogous theorem for the continuous torus of the original Junta theorem proved by Friedgut in the case of the Boolean cube. Analogous statements have been established recently in discrete cases…

This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our…