Probabilistic inequalities for independent random variables and martingales play a prominent role in many different areas of mathematical research, such as harmonic analysis, probability theory, Banach space geometry and the study of symmetric function spaces. In the recent years, many of these classical probabilistic inequalities have been generalized to the context of noncommutative Lp-spaces...

In this paper, we study some functional inequalities (such as Poincaré inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy inequalities) for reversible nearest-neighbor Markov processes on a connected finite graph by means of (random) path method. We provide estimates of the involved c...

This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces. These are combined with eigenvalue estimates to give good bounds on the rate of convergence to stationarity for finite Markov chains whose underlying graph has moderate volume growth. Roughly, for such chains, order (diameter) 2 steps are necessary and suffice to reach stationarity. We consider l...

In this paper, we establish some analytic inequalities for Schurconvex functions that are made of solutions of a second order nonlinear differential equation. We apply these analytic inequalities to obtain some geometric inequalities.

We derive transport-entropy inequalities for mixed binomial point processes, and Poisson processes. show that when the finite intensity measure satisfies a Talagrand transport inequality, law of process also type inequality. (with arbitrary ?-finite measure) always universal inequality à la Marton. explore consequences these in terms concentration modified logarithmic Sobolev inequalities. In p...

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

We propose two systematic methods to describe the differential property of an S-box with linear inequalities based on logical condition modelling and computational geometry respectively. In one method, inequalities are generated according to some conditional differential properties of the S-box; in the other method, inequalities are extracted from the H-representation of the convex hull of all ...