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We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…

In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain desintegration. This is a desintegration with…

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

We consider a particle moving in one dimension, its velocity being a reversible diffusion process, with constant diffusion coefficient, of which the invariant measure behaves like $(1+|v|)^{-\beta}$ for some $\beta>0$. We prove that, under…

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…

A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma…

We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type…

We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

The quantitative long time behavior of absorbing, finite, irreducible Markov processes is considered. Via Doob transforms, it is shown that only the knowledge of the ratio of the values of the underlying first Dirichlet eigenvector is…

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…

The Mott critical point between a metal and a correlated insulator has usually been studied via density or spin density bosonic mode fluctuations according to the standard Ginzburg-Landau-Wilson phase transition paradigm. A moment's…

Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…

Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the…

We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…

We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasi-periodic…

A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new…

The di-fermion angular distribution observed in decays of inclusively produced vector particles is characterized by two frame-independent observables, reflecting the average spin-alignment of the produced particle and the magnitude of…

Periodic driving can tune the quasistatic properties of quantum matter. A well-known example is the dynamical modification of tunneling by an oscillating electric field. Here we show experimentally that driving the phasonic degree of…