Related papers: On the dynamical evolution of randomness Part A: R…
We study an extension of the generalized excited random walk (GERW) on $\mathbb{Z}^d$ introduced in [Ann. Probab. 40 (5), 2012, [7]] by Menshikov, Popov, Ram\'irez and Vachkovskaia. Our extension consists in studying a version of the GERW…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
Behavior in the context of game theory is described as a natural process that follows the 2nd law of thermodynamics. The rate of entropy increase as the payoff function is derived from statistical physics of open systems. The thermodynamic…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
Recently Khmaladze has shown how to `rotate' one empirical process to another. This paper is the first to apply this transform when successive data points are generated by a single distributional family, but with covariates varying over the…
Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer…
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
The random reversal graph offers new perspectives, allowing to study the connectivity of genomes as well as their most likely distance as a function of the reversal rate. Our main result shows that the structure of the random reversal graph…
We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit…
Is there a joint distribution of $n$ random variables over the natural numbers, such that they always form an increasing sequence and whenever you take two subsets of the set of random variables of the same cardinality, their distribution…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…