Related papers: A short note on Godbersen's Conjecture
We propose a new and rather stringent criterion for testing the goodness of fit between a theory and experiment. It is motivated by the paradox that the criterion on \chi^2 for testing a theory is much weaker than the criterion for finding…
It is widely believed that the assumption of homogeneity is a good zero{\it th} order approximation for the expansion of our Universe. We analyze the correction due to subhorizon inhomogeneous gravitational fields. While at early times this…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
The goal of this short note is to discuss the relation between Kullback--Leibler divergence and total variation distance, starting with the celebrated Pinsker's inequality relating the two, before switching to a simple, yet (arguably) more…
We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the…
We comment on different results from three recent effective potential calculations of the Higgs mass lower bound.
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
This is a survey on Kawaguchi-Silverman conjecture.
In this note we prove a more general (and topological) version of Gr\"unbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the group of similarities, Gr\"unbaum's…
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of…
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical…