Related papers: Effective quenched linear response for random dyna…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging.…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
In this work we present a reduction result for discrete time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly…
We present linear response theories in the continuum capable of describing continuum spectra and dynamical correlations of finite systems with no spatial symmetry. Our formulation is essentially the same as the continuum random-phase…
In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…
We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear…
Coherent diffractive imaging has enabled the structural analysis of individual free nanoparticles in a single shot and offers the tracking of their light induced dynamics with unprecedented spatial and temporal resolution. The retrieval of…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
We consider, in more details than it was done previously, the effective low-energy behavior in the quantum theory of a light scalar field coupled to another scalar with much larger mass. The main target of our work is an IR decoupling of…
The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to…
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The…
We study rates of mixing for small random perturbations of one dimensional Lorenz maps. Using a random tower construction, we prove that, for Holder observables, the random system admits exponential rates of quenched correlation decay.
Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from…