This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic ...

Classically, finite modified logarithmic Sobolev inequalities are used to deduce a differential inequality for the evolution of the relative entropy with respect to the invariant measure. We will ...

Description: Such topics as polynomial functions and equations, exponential and logarithmic functions, determinants, systems of equations and inequalities, mathematical induction, the binomial theorem ...

Matrix inequalities and convex functions constitute a central theme in modern mathematical analysis, with far‐reaching implications across numerical analysis, optimisation, quantum information, and ...