Publications related to On the density of the supremum of the solution to the linear stochastic heat equation

The elliptical Ornstein-Uhlenbeck process

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are obse ...

INT PRESS BOSTON, INC2023

Resource aware pricing for electric vehicle charging

Nils Gustav Nilsson

Electric vehicle charging facilities offer their capacity constrained electric charge and parking to users for a fee. As electric vehicle adoption grows, so too does the potential for excessive resource utilization. In this paper, we study how prices set b ...

PERGAMON-ELSEVIER SCIENCE LTD2023

CONVERGENCE AND NONCONVERGENCE OF SCALED SELF-INTERACTING RANDOM WALKS TO BROWNIAN MOTION PERTURBED AT EXTREMA

Thomas Mountford

We use generalized Ray-Knight theorems, introduced by B. Toth in 1996, together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusively scaled sel ...

Cleveland2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, Cheuk Yin Lee, David Jean-Michel Candil

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

New York2023

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Frédéric Courbin, Gianluca Castignani, Jean-Luc Starck, Maurizio Martinelli, Austin Chandler Peel, Yi Wang, Richard Massey, Fabio Finelli, Marcello Farina

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale ...

EDP SCIENCES S A2023

Polynomial-time universality and limitations of deep learning

Emmanuel Abbé

The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...

WILEY2023

Engineering random spin models with atoms in a high-finesse cavity

Jean-Philippe Brantut

Random spin models play a key role in our understanding of disorder and complex many-body systems. Two all-to-all interacting, disordered models have now been realized using a cavity quantum electrodynamics platform. All-to-all interacting, disordered quan ...

NATURE PORTFOLIO2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Philadelphia2023

Distributional Regression and Autoregression via Optimal Transport

Laya Ghodrati

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

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EPFL2023

On the density of the supremum of the solution to the linear stochastic heat equation

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The elliptical Ornstein-Uhlenbeck process

Resource aware pricing for electric vehicle charging

CONVERGENCE AND NONCONVERGENCE OF SCALED SELF-INTERACTING RANDOM WALKS TO BROWNIAN MOTION PERTURBED AT EXTREMA

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Polynomial-time universality and limitations of deep learning

Engineering random spin models with atoms in a high-finesse cavity

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Distributional Regression and Autoregression via Optimal Transport

Resource aware pricing for electric vehicle charging

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

The elliptical Ornstein-Uhlenbeck process

Engineering random spin models with atoms in a high-finesse cavity

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Distributional Regression and Autoregression via Optimal Transport

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

CONVERGENCE AND NONCONVERGENCE OF SCALED SELF-INTERACTING RANDOM WALKS TO BROWNIAN MOTION PERTURBED AT EXTREMA

Polynomial-time universality and limitations of deep learning