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A note on a maximal Bernstein inequality
Bernstein inequality dependent sums maximal inequality mixing partial sums
2011/9/13
Abstract: We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also val...
A simple variance inequality for U-statistics of a Markov chain with applications
U-statistics Markov chains Inequalities Limit theorems Law of large numbers
2011/9/5
Abstract: We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend ...
Vector-valued decoupling and the Burkholder-Davis-Gundy inequality
vector-valued decoupling inequalities tangent sequences UMD Banach spaces vector-valued stochastic integration
2011/9/2
Abstract: Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach sp...
A rank inequality for the knot Floer homology of double branched covers
the knot Floer homology double branched covers Geometric Topology
2011/9/1
Abstract: Given a knot $K$ in $S^3$, let $\Sigma(K)$ be the double branched cover of $S^3$ over $K$. We show there is a spectral sequence whose $E^1$ page is $(\hat{HFK}(\Sigma(K), K) \otimes V^{n-1})...
Bohr's inequality revisited
Bohr's inequality revisited Functional Analysis Operator Algebras
2011/8/26
Abstract: We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators relate...
Discrete Laguerre-Sobolev expansions: A Cohen type inequality
Laguerre polynomials Laguerre–Sobolev type polynomials Cohen type inequality Bessel functions
2011/8/25
Abstract: 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 expa...
An inequality for the distance between densities of free convolutions
densities of free convolutions inequality Probability
2011/8/24
Abstract: It is shown that under some conditions the distance between densities of free convolutions of two pairs of probability measures is smaller than the maximum of the Levy distance between the c...
Numerically explicit version of the Pólya--Vinogradov inequality
Numerically explicit version the Pólya--Vinogradov inequality
2011/8/23
Abstract: In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obt...
A natural derivative on [0,n] and a binomial Poincaré inequality
natural derivative binomial Poincaré inequality Probability
2011/8/22
Abstract: We consider probability measures supported on a finite discrete interval $[0,n]$. We introduce a new finitedifference operator $\nabla_n$, defined as a linear combination of left and right f...
On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$
differential forms semialgebraic set Geometric Topology
2011/8/23
Abstract: We study Poincar\'e type $L^p$ inequality on a compact semialgebraic subset of $\R^n$ for $p>>1$. First we derive a local inequality by using a Lipschitz deformation retraction with estimate...
Abstract: The main observation of this note is that the Lebesgue measure $\mu$ in the Tur\'an-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant $\omega ...
A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with th...
Robin inequality for $7-$free integers
Dedekind function Robin inequality Riemann Hypothesis Primorial numbers
2011/1/17
Recall that an integer is t−free iff it is not divisible by pt for some prime p. We give a method to check Robin inequality (n) < e n log log n, for t−free integers n and apply it for t =...
A sharp correlation inequality with an application to almost sure local limit theorem
Correlation inequality i.i.d. random variables lattice distributed
2011/2/21
We prove a new sharp correlation inequality for sums of i.i.d.square integrable lattice distributed random variables. We also apply it to establish an almost sure local limit theorem for iid square in...
A quantitative isoperimetric inequality for fractional perimeters
quantitative isoperimetric inequality fractional perimeters
2011/1/14
Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here ...