Related papers: Local random potentials of high differentiability …

The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…

The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…

We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble statistics across several network architectures and datasets.…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…

This paper is concerned with two related types of directed polymers in a random medium. The first one is a d-dimensional Brownian motion living in a random environment which is Brownian in time and homogeneous in space. The second is a…

This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…

Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering…

We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable…

We consider a spinless particle moving in a random potential on a d-dimensional torus. Introducing the gradient of the logarithm of the wave-function transforms the time independent Schroedinger equation into a stochastic differential…

Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…

Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a new method for computing the spectral functions in…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Amp\`ere equation, and mean…

For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…

A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential function. Under very mild extra technical conditions, we first…

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…

While there already exist randomized subspace Newton methods that restrict the search direction to a random subspace for a convex function, we propose a randomized subspace regularized Newton method for a non-convex function {and more…

Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…