Related papers: On $\mathcal H^1$ and entropic convergence for con…
A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited assumptions about the transport field, which might be…
Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a (possibly non-symmetric) Markov process yields…
A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable $\eps$. The coefficients of the expansion around the noiseless ($\eps = 0$) limit were calculated up to…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the…
On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…
We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of…
We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional…
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion processes. As a consequence, we…
We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate.…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
In the present work we derive a Central Limit Theorem for sequences of Hilbert-valued Piecewise Deterministic Markov process models and their global fluctuations around their deterministic limit identified by the Law of Large Numbers. We…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a…
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible…
We compute the Hamiltonian and Lagrangian associated to the large deviations of the trajectory of the empirical distribution for independent Markov processes, and of the empirical measure for translation invariant interacting Markov…
Expressions for (EPI Shannon type) Divergence-Power Inequalities (DPI) in two cases (time-discrete and band-limited time-continuous) of stationary random processes are given. The new expressions connect the divergence rate of the sum of…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…