Publications related to An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Let T be a measure-preserving Zℓ-action on the probability space (X,B,μ), let q1,…,qm:R→Rℓ be vector polynomials, and let f0,…,fm∈L∞⁡(X). For any ϵ>0 and multicorrelation sequences of the form α⁡(n)=∫Xf0⋅T⌊q1⁡(n)⌋⁢f1⋯T⌊qm⁡(n)⌋⁢fmd⁢μ we show that there exis ...

2021

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

MATHICSE Technical Report : Analysis of a class of Multi-Level Markov Chain Monte Carlo algorithms based on Independent Metropolis-Hastings

Fabio Nobile, Juan Pablo Madrigal Cianci

In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solvin ...

MATHICSE2021

Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema

Thomas Mountford

We consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motio ...

2021

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

2020

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

Fractional extreme distributions

Thomas Simon, Lotfi Boudabsa

We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...

2020

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Daniel Maria Busiello, Deepak Gupta

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the th ...

2020

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

Graph Chatbot

Chat with Graph Search

Structure of multicorrelation sequences with integer part polynomial iterates along primes

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

MATHICSE Technical Report : Analysis of a class of Multi-Level Markov Chain Monte Carlo algorithms based on Independent Metropolis-Hastings

Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Normalized Gaussian path integrals

Fractional extreme distributions

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

A Local Law for Singular Values from Diophantine Equations

Strong convergence of multivariate maxima

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Normalized Gaussian path integrals

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Fractional extreme distributions

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema

A Local Law for Singular Values from Diophantine Equations

Strong convergence of multivariate maxima

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

MATHICSE Technical Report : Analysis of a class of Multi-Level Markov Chain Monte Carlo algorithms based on Independent Metropolis-Hastings