Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Melbourne, James"'
We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent random vecto
Externí odkaz:
http://arxiv.org/abs/2406.04200
Inspired by the approach of Ivanisvili and Volberg towards functional inequalities for probability measures with strictly convex potentials, we investigate the relationship between curvature bounds in the sense of Bakry-Emery and local functional ine
Externí odkaz:
http://arxiv.org/abs/2403.00969
Learning causal effects from data is a fundamental and well-studied problem across science, especially when the cause-effect relationship is static in nature. However, causal effect is less explored when there are dynamical dependencies, i.e., when d
Externí odkaz:
http://arxiv.org/abs/2309.02571
We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-con
Externí odkaz:
http://arxiv.org/abs/2309.01840
Autor:
Jaramillo, Arturo, Melbourne, James
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$. We discuss
Externí odkaz:
http://arxiv.org/abs/2210.11632
A remarkable conjecture of Feige (2006) asserts that for any collection of $n$ independent non-negative random variables $X_1, X_2, \dots, X_n$, each with expectation at most $1$, $$ \mathbb{P}(X < \mathbb{E}[X] + 1) \geq \frac{1}{e}, $$ where $X = \
Externí odkaz:
http://arxiv.org/abs/2208.12702
Autor:
Marsiglietti, Arnaud, Melbourne, James
We utilize and extend a simple and classical mechanism, combining log-concavity and majorization in the convex order to derive moments, concentration, and entropy inequalities for certain classes of log-concave distributions.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2205.08293
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also derive sever
Externí odkaz:
http://arxiv.org/abs/2111.06997
Autor:
Melbourne, James, Roberto, Cyril
We introduce a transport-majorization argument that establishes a majorization in the convex order between two densities, based on control of the gradient of a transportation map between them. As applications, we give elementary derivations of some d
Externí odkaz:
http://arxiv.org/abs/2110.03641
Autor:
Melbourne, James, Roberto, Cyril
We prove a quantitative form of the celebrated Ball's theorem on cube slicing in $\mathbb{R}^n$ and obtain, as a consequence, equality cases in the min-entropy power inequality. Independently, we also give a quantitative form of Khintchine's inequali
Externí odkaz:
http://arxiv.org/abs/2109.03946