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Gaussian noise stability results have recently played an important role in proving results in hardness of approximation in computer science and in the study of voting schemes in social choice. We prove a new Gaussian noise stability result…

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…

We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Cr{\'e}pey, Jeanblanc, and Wu (2013) are invariance times in the sense of Cr{\'e}pey and Song (2017), with related invariance probability…

Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…

We show that the long-standing problem of gauge dependence of the effective potential arises due to the factorisation of the determinant of operators, which is invalid when we take the zeta-regularised trace of the operators. We show by…

This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary…

We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone…

In this paper, we consider the self-similar measure $\nu_\lambda=\mathrm{law}\left(\sum_{j \geq 0} \xi_j \lambda^j\right)$ on $\mathbb{R}$, where $|\lambda|<1$ and the $\xi_j \sim \nu$ are independent, identically distributed with respect…

A formulation of the generalized minimal output entropy conjecture for Gaussian channels is presented. It asserts that, for states with fixed input entropy, the minimal value of the output entropy of the channel (i.e. the minimal output…

Park and Pham's recent proof of the Kahn-Kalai conjecture was a major breakthrough in the field of graph and hypergraph thresholds. Their result gives an upper bound on the threshold at which a probabilistic construction has a $1-\epsilon$…

We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality itself and not the actual flow, allowing for somewhat…

Gaussian periods are cyclotomic integers with a long history in number theory and connections to problems in combinatorics. We investigate the asymptotic behavior of the absolute norm of a Gaussian period and provide a rate of convergence…

We consider some elementary aspects of the geometry of the space of probability measures endowed with Wasserstein distance. In such a setting, we discuss the various terms entering Perelman's shrinker entropy, and characterize two new…

Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author,…

In the face of mounting numerical evidence, Metlitski and Grover [arXiv:1112.5166] have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a sub-leading contribution to the entanglement…

The hypothesis of the random flow of time is considered. To do this, the concepts of microscopic random time and macroscopic mean time, as well as random modular time are introduced. The possibilities of experimental verification of the…

In this work, we obtain a short time existence result for harmonic map heat flow coupled with a smooth family of complete metrics in the domain manifold. Our results generalize short time existence results for harmonic map heat flow by…

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to…

Let $u,v \in \mathbb{R}^\Omega_+$ be positive unit vectors and $S\in\mathbb{R}^{\Omega\times\Omega}_+$ be a symmetric substochastic matrix. For an integer $t\ge 0$, let $m_t = \smash{\left\langle v,S^tu\right\rangle}$, which we view as the…