Related papers: Statistics as a dynamical attractor
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
The image of physics is connected with simple "mechanical" deterministic events: that an apple always falls down, that force equals mass times acceleleration. Indeed, applications of such concept to social or historical problems go back two…
We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the…
By using a fonctionelle of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general method. The essential equivalence between the MaxEnt process of the most…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the…
We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in…
This paper is devoted to the study of the asymptotic dynamics of the stochastic damped sine-Gordon equation with homogeneous Neumann boundary condition. It is shown that for any positive damping and diffusion coefficients, the equation…
Understanding how hydrodynamics emerges rapidly in the medium produced by relativistic heavy-ion collisions remains a key theoretical challenge. While the attractor solution -- manifesting as a non-thermal fixed point during the early…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$. We would like to emphasize that we do not use the usual cohomology…
We establish the effective {\em finite dimensionality} of the dynamics corresponding to a flow-plate interaction PDE model arising in aeroelasticity: a nonlinear panel, in the absence of rotational inertia, immersed in an inviscid potential…
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely,…
A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…