Publications associées à Hypothèse ergodique

Additive and geometric transversality of fractal sets in the integers

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Andrea Zanoni, Grigorios A. Pavliotis

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

Siam Publications2024

Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation

Valentin Marc Schmutz

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This additional variable ca ...

2022

HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

Juan Pablo Madrigal Cianci

This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP). The first hierarchical method we present is base ...

EPFL2022

Multi-Level Monte Carlo Methods for Uncertainty Quantification and Risk-Averse Optimisation

Sundar Subramaniam Ganesh

This work aims to study the effects of wind uncertainties in civil engineering structural design. Optimising the design of a structure for safety or operability without factoring in these uncertainties can result in a design that is not robust to these per ...

EPFL2022

Unfreezing Social Navigation: Dynamical Systems based Compliance for Contact Control in Robot Navigation

Aude Billard, Diego Felipe Paez Granados, Vaibhav Gupta

Large efforts have focused on ensuring that the controllers for mobile service robots follow proxemics and other social rules to ensure both safe and socially acceptable distance to pedestrians. Nonetheless, involuntary contact may be unavoidable when the ...

IEEE2022

Many-body localization in a fragmented Hilbert space

Loïc Jean Pierre Herviou

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...

2021

Generalized parallel tempering on Bayesian inverse problems

Fabio Nobile, Juan Pablo Madrigal Cianci

In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-timeMarkov chainMonteCarlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so ...

2021

Macroscopic polarization in the nominally ergodic relaxor state of lead magnesium niobate

Dragan Damjanovic, Lukas Riemer, Yang Li, Kanghyun Chu, Brahim Dkhil

Macroscopic polarity and its dynamic response to external electric fields and temperature in the nominally ergodic relaxor phase of pristine lead magnesium niobate crystals and ceramics, Pb(Mg1/3Nb2/3)O3 (PMN), were investigated. Dynamic pyroelectric measu ...

AIP American Institute of Physics2020

An Ergodic Theory of Binary Operations-Part II: Applications to Polarization

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Institute of Electrical and Electronics Engineers2017