Related papers: The law of series
Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance.…
We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
This note addresses the relevance of rare events in system dynamics, inspired by Jill North reflections on the origin of the arrow of time in thermodynamics. After identifying the existence of rare events, characterized by a Pareto…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each…
Given an ergodic dynamical system $(X,T,\mu)$, and $U\subset X$ measurable with $\mu (U)>0$, let $\mu (U)\tau_U(x)$ denote the normalized hitting time of $x\in X$ to $U$. We prove that given a sequence $(U_n)$ with $\mu (U_n)\to 0$, the…
The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial…
In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set $A \subset \mathbb{R}^d.$ This Poisson process of cylinders is…
We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times…
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…
Prevalent in many real-world settings such as healthcare, irregular time series are challenging to formulate predictions from. It is difficult to infer the value of a feature at any given time when observations are sporadic, as it could…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…