相关论文: A Gordon-Chevet type Inequality
This note comments on parts of "New 5-designs." We cite Chebotarev's theorem; we correct some minor errors and we clarify our proof of the Gleason-Prange theorem.
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The…
A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural…
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the…
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
In this note we are concerned about the generalization of the GHS inequality for the Potts model. We also obtain by a different method the proof of the GHS inequality for the Ising model. We take advantage of a polynomial expansion and we…
An Ostrowski type integral inequality for convex functions and applications for quadrature rules and integral means are given. A refinement and a counterpart result for Hermite-Hadamard inequalities are obtained and some inequalities for…
We analyse an analog of the entropy-power inequality for the weighted entropy.
The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial…
C. Markett proved a Cohen type inequality for the classical Laguerre expansions in the appropriate weighted $L^{p}$ spaces. In this paper, we get a Cohen type inequality for the Fourier expansions in terms of discrete Laguerre--Sobolev…
In this note we prove an inequality involving primes and the product of consecutive primes.
In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…
We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this…
We draw attention to an easy-to-remember explanation for the graded-case inequality of Golod and Shafarevich. We review some of the classic material on this inequality.
We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.
Suppose $(X_t)_{t \in T}$ is a Gaussian process indexed by some arbitrary set $T:$ the random variable $\sup_{t \in T}{X_t}$ can be very intricate and bounding its expectation is a natural step towards understanding it. Sudakov-Fernique…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
Without higher moment assumptions, this note establishes the decay of the Kolmogorov distance in a central limit theorem for L\'evy processes. This theorem can be viewed as a continuous-time extension of the classical random walk result by…
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.