Related papers: On Eagleson's theorem in the non-stationary setup
We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain small for exponentially long times. The result is uniform with respect to $c \geq…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is…
We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding…
In the framework of stochastic zero-sum differential games, we establish a verification theorem, inspired by those existing in stochastic control, to provide sufficient conditions for a pair of feedback controls to form a Nash equilibrium.…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…
It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy…
We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\mu$ converge to $\mu$ in the total variation distance. In addition we show…
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
This paper introduces a new method to tackle the issue of the almost sure convergence of stochastic approximation algorithms defined from a differential inclusion. Under the assumption of slowly decaying step-sizes, we establish that the…
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…
Walsh has recently proved the norm convergence of all nonconventional ergodic averages involving polynomial sequences in discrete nilpotent acting groups. He deduces this convergence from an equivalent, `finitary' assertion of stability…
We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behavior of iterates is described by a…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in…
Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we call \emph{Elser…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…