Related papers: The strong data processing inequality under the he…
We consider a system of $d$ non-linear stochastic fractional heat equations in spatial dimension $1$ driven by multiplicative $d$-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and…
We study the problem of characterizing the stability of Kullback-Leibler (KL) divergence under Gaussian perturbations beyond Gaussian families. Existing relaxed triangle inequalities for KL divergence critically rely on the assumption that…
We calculate the probability distribution $P({\bf k})$ for a heavy quark with velocity $v$ propagating through strongly coupled $\mathcal{N}=4$ SYM plasma in the 't Hooft limit at a temperature $T$ to acquire a momentum ${\bf k}$ due to…
We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. First, we provide results that give upper estimates in a situation when the corresponding jump measure is allowed to be highly…
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
Turbulence is a complex phenomenon that plays a critical role in the interstellar medium (ISM). Previous simulations and observations show that the probability density function (PDF) of gas density in isothermal and compressible systems…
In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the…
The performance of machine learning classification algorithms are evaluated by estimating metrics, often from the confusion matrix, using training data and cross-validation. However, these do not prove that the best possible performance has…
In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\sigma_\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as…
We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…
We consider the standard first passage percolation model in $\ZZ^d$ for $d\geq 2$ and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a…
The derivation of Student's pdf from superstatistics is a mere coincidence due to the choice of the $\chi^2$ distribution for the inverse temperature which is actually the Maxwell distribution for the speed. The difference between the…
In this note, we prove a sharp large derivation principle (LDP) for the cubic nonlinear Schr\"odinger equation with Gaussian random initial data in Fourier Lebesgue spaces. As a consequence, we improve the exponential decay condition in…
We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an…