Renaud Raquépas

Journal Article Canadian Journal of Mathematics · June 1, 2025 We generalize to a broader class of decoupled measures a result of Ziv and Merhav on universal estimation of the specific cross (or relative) entropy, originally for a pair of multilevel Markov measures. Our generalization focuses on abstract decoupling co ... Full text Cite

Quenched Large Deviations of Birkhoff Sums Along Random Quantum Measurements

Journal Article Annales Henri Poincare · January 1, 2025 We prove a quenched version of the large deviation principle for Birkhoff-like sums along a sequence of random quantum measurements driven by an ergodic process. We apply the result to the study of entropy production in the two-time measurement framework. ... Full text Cite

Large Deviations of Return Times and Related Entropy Estimators on Shift Spaces

Journal Article Communications in Mathematical Physics · June 1, 2024 We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some decoupling conditions wh ... Full text Cite

The large-time and vanishing-noise limits for entropy production in nondegenerate diffusions

Journal Article Annales De L Institut Henri Poincare B Probability and Statistics · February 1, 2024 We investigate the behaviour of a family of entropy production functionals associated to stochastic differential equations of the form (Formula Presented) where b is a globally Lipschitz nonconservative vector field keeping the system out of equilibrium, w ... Full text Cite

Ziv-Merhav Estimation for Hidden-Markov Processes

Conference IEEE International Symposium on Information Theory Proceedings · January 1, 2024 We present a proof of strong consistency of a Ziv-Merhav-type estimator of the cross entropy rate for pairs of hidden-Markov processes. Our proof strategy has two novel aspects: the focus on decoupling properties of the laws and the use of tools from the t ... Full text Cite

On a waiting-time result of Kontoyiannis: Mixing or decoupling?

Journal Article Stochastic Processes and their Applications · December 1, 2023 We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large dev ... Full text Cite

A gapped generalization of Kingman’s subadditive ergodic theorem

Journal Article Journal of Mathematical Physics · June 1, 2023 We state and prove a generalization of Kingman’s ergodic theorem on a measure-preserving dynamical system ( X , F , μ , T ) where the μ-almost sure subadditivity condition fn+m ≤ fn + fm◦Tn is relaxed to a μ-almo ... Full text Cite

Recurrence times, waiting times and universal entropy production estimators

Journal Article Letters in Mathematical Physics · February 1, 2023 The universal typical-signal estimators of entropy and cross-entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal typical-signal esti ... Full text Cite

Fermionic Walkers Driven Out of Equilibrium

Journal Article Journal of Statistical Physics · August 1, 2021 We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of ... Full text Cite

Exponential mixing under controllability conditions for SDEs driven by a degenerate Poisson noise

Journal Article Stochastic Processes and their Applications · August 1, 2021 We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions on the distribut ... Full text Cite

On Fermionic walkers interacting with a correlated structured environment

Journal Article Letters in Mathematical Physics · January 1, 2020 We study the large-time behaviour of a sample S consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions E through an exchange of particles in preferred states. We describe the asymptotic state ... Full text Cite

Control of Fluctuations and Heavy Tails for Heat Variation in the Two-Time Measurement Framework

Journal Article Annales Henri Poincare · February 5, 2019 We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier ... Full text Cite

A Note on Harris’ Ergodic Theorem, Controllability and Perturbations of Harmonic Networks

Journal Article Annales Henri Poincare · February 5, 2019 We show that elements of control theory, together with an application of Harris’ ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of quasi-harmonic classical osc ... Full text Cite

Landauer’s Principle for Trajectories of Repeated Interaction Systems

Journal Article Annales Henri Poincare · July 1, 2018 We analyse Landauer’s principle for repeated interaction systems consisting of a reference quantum system S in contact with an environment E which is a chain of independent quantum probes. The system S interacts with each probe sequentially, for a given du ... Full text Cite

Landauer’s Principle in Repeated Interaction Systems

Journal Article Communications in Mathematical Physics · January 1, 2017 We study Landauer’s Principle for Repeated Interaction Systems (RIS) consisting of a reference quantum system S in contact with a structured environment E made of a chain of independent quantum probes; S interacts with each probe, for a fixed duration, in ... Full text Cite