Concept

Laplace's method

Related publications (10)

Unraveling looping efficiency of stochastic Cosserat polymers

Understanding looping probabilities, including the particular case of ring closure or cyclization, of fluctuating polymers (e.g., DNA) is important in many applications in molecular biology and chemistry. In a continuum limit the configuration of a polymer ...

AMER PHYSICAL SOC2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Support and approximation properties of Hermite splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

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

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

SPRINGER2020

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

SPRINGER/PLENUM PUBLISHERS2020

Precision theoretical methods for large-scale structure of the Universe

Mikhail Ivanov

We develop new analytic methods to accurately describe the formation of cosmic large-scale structure. These methods are based on the path integral formalism and allows one to efficiently address a number of long-standing problems in the field. We describe ...

EPFL2019

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxima ...

2013

Gaussian upper density estimates for spatially homogeneous SPDEs

We consider a general class of SPDEs in mathbb{R}^d driven by a Gaussian spatially homogeneous noise which is white in time. We provide sufficient conditions on the coefficients and the spectral measure associated to the noise ensuring that the density of ...

2012

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxi ...

arxiv.org2010

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The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018