73 citations · 160 across the 24 of their papers we have counts for
27 papers
A note on the Littlewood-Offord problem for discrete log-concave distributions
Arnaud Marsiglietti, James Melbourne
We present an extension of the famous Littlewood-Offord problem when Bernoulli distributions are replaced with discrete log-concave distributions. A variant of the Littlewood-Offor…
Causal Structure Recovery of Linear Dynamical Systems: An FFT based Approach
Mishfad Shaikh Veedu, James Melbourne, Murti V. Salapaka
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 effec…
Quantitative limit theorems via relative log-concavity
Arturo Jaramillo, James Melbourne
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 and $ν…
On a Conjecture of Feige for Discrete Log-Concave Distributions
Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti +1
A remarkable conjecture of Feige (2006) asserts that for any collection of independent non-negative random variables , each with expectation at most ,…
Concentration inequalities for log-concave sequences
Arnaud Marsiglietti, James Melbourne
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entr…
A discrete complement of Lyapunov's inequality and its information theoretic consequences
James Melbourne, Gerardo Palafox-Castillo
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…
Transport-majorization to analytic and geometric inequalities
James Melbourne, Cyril Roberto
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 b…
Quantitative form of Ball's Cube slicing in and equality cases in the min-entropy power inequality
James Melbourne, Cyril Roberto
We prove a quantitative form of the celebrated Ball's theorem on cube slicing in and obtain, as a consequence, equality cases in the min-entropy power inequality. In…
Concentration Inequalities for Ultra Log-Concave Distributions
Heshan Aravinda, Arnaud Marsiglietti, James Melbourne
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration b…
Bernoulli sums and Rényi entropy inequalities
Mokshay Madiman, James Melbourne, Cyril Roberto
We investigate the Rényi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the Rén…
Strongly Convex Divergences
James Melbourne
We consider a sub-class of the -divergences satisfying a stronger convexity property, which we refer to as strongly convex, or -convex divergences. We derive new and old rela…
Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension
James Melbourne, Govind Saraswat, Vivek Khatana +2
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide…
Concentration functions and entropy bounds for discrete log-concave distributions
Sergey G. Bobkov, Arnaud Marsiglietti, James Melbourne
Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain varian…
Hindering loads prompt clustered configurations that enhance stability during cargo transport by multiple Kinesin-1
Shreyas Bhaban, Rachit Srivastava, James Melbourne +2
Transport of intracellular cargo is often mediated by teams of molecular motors that function in a chaotic environment under varying conditions. We show that the motors have unique…
Reversals of Rényi Entropy Inequalities under Log-Concavity
James Melbourne, Tomasz Tkocz
We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Sh…
Geometric and Functional Inequalities for Log-concave Probability Sequences
Arnaud Marsiglietti, James Melbourne
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the…
Further investigations of Rényi entropy power inequalities and an entropic characterization of s-concave densities
Jiange Li, Arnaud Marsiglietti, James Melbourne
We investigate the role of convexity in Rényi entropy power inequalities. After proving that a general Rényi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails…
Realizing Information Erasure in Finite Time
James Melbourne, Saurav Talukdar, Murti Salapaka
In this article, we focus on erasure of a bit of information in finite time. Landauer's principle states that the average heat dissipation due to erasure of information is k_B T ln…
An Exact Upper Bound on the Lebesgue Constant and The -Rényi Entropy Power Inequality for Integer Valued Random Variables
Peng Xu, Mokshay Madiman, James Melbourne
In this paper, we proved an exact asymptotically sharp upper bound of the Lebesgue Constant (i.e. the norm of Dirichlet kernel) for . As an application, we also…
Rearrangement and Prekopa-Leindler type inequalities
James Melbourne
We investigate the interactions of functional rearrangements with Prekopa-Leindler type inequalities. It is shown that that a general class of integral inequalities tighten on rear…
Error Bounds on a Mixed Entropy Inequality
James Melbourne, Saurav Talukdar, Shreyas Bhaban +1
Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality invol…
The Differential Entropy of Mixtures: New Bounds and Applications
James Melbourne, Saurav Talukdar, Shreyas Bhaban +2
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy o…
Designing Memory Bits with Dissipation lower than the Landauer's Bound
Saurav Talukdar, Shreyas Bhaban, James Melbourne +1
A Brownian particle in a symmetric double well potential is used as a representation for a single bit memory, where, the location of the particle in either well denotes one of the…
On the entropy power inequality for the Rényi entropy of order [0,1]
Arnaud Marsiglietti, James Melbourne
Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive Rényi entropy power…