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A word-valued source $\mathbf{Y} = Y_1,Y_2,...$ is discrete random process that is formed by sequentially encoding the symbols of a random process $\mathbf{X} = X_1,X_2,...$ with codewords from a codebook $\mathscr{C}$. These processes…
We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they…
We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
Language models (LMs) are trained on billions of tokens in an attempt to recover the true language distribution. Still, vanilla random sampling from LMs yields low quality generations. Decoding algorithms attempt to restrict the LM…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
We consider reparametrizations of Heisenberg nilflows. We show that if a Heisenberg nilflow is uniquely ergodic, all non-trivial time-changes within a dense subspace of smooth time-changes are mixing. Equivalently, in the language of…
If a macroscopic (random) classical system is put into a random state in phase space, it will of course the most likely have an almost maximal entropy according to second law of thermodynamics. We will show, however, the following theorem:…
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of…
Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
A plug-in estimator of entropy is the entropy of the distribution where probabilities of symbols or blocks have been replaced with their relative frequencies in the sample. Consistency and asymptotic unbiasedness of the plug-in estimator…
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system…
We consider non-ergodic class of stationary real harmonizable symmetric $\alpha$-stable processes $X=\left\{X(t):t\in\mathbb{R}\right\}$ with a finite symmetric and absolutely continuous control measure. We refer to its density function as…
We prove a multiplicative ergodic theorem for bistochastic completely positive (bcp) linear cocycles acting on finite-dimensional matrix algebras, giving an invariant splitting described explicitly in terms of the multiplicative domains of…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…