Related papers: The recurrence function of a random Sturmian word
A correlation is a binary vector that encodes all possible positions of overlaps of two words, where an overlap for an ordered pair of words (u,v) occurs if a suffix of word u matches a prefix of word v. As multiple pairs can have the same…
The results of the study provide guidelines for the development and applications of algorithms. When the number of steps for calculating an assumption tends to infinity, probability theory can be applied to predict whether the assumption…
Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
We consider sequences of polynomials that satisfy differential-difference recurrences. Polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence…
We describe and experimentally evaluate a method for automatically clustering words according to their distribution in particular syntactic contexts. Deterministic annealing is used to find lowest distortion sets of clusters. As the…
The prefix palindromic length $p_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. This function is surprisingly difficult to…
For words of length $n$, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, $q$--analogues for these…
We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…
We investigate the probability distributions of the recurrence intervals $\tau$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock…
We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number…
The present study uses a computational approach to examine the role of semantic constraints in normal reading. This methodology avoids confounds inherent in conventional measures of predictability, allowing for theoretically deeper accounts…
Given a random walk $(S_n)$ with typical step distributed according to some fixed law and a fixed parameter $p \in (0,1)$, the associated positively step-reinforced random walk is a discrete-time process which performs at each step, with…
For random maps, the expected value of the order (i.e. the period of the sequence of compositional iterates) is approximated asymptotically. It is much smaller than the expected value for the product of the cycle lengths.
Any infinite uniformly recurrent word ${\bf u}$ can be written as concatenation of a finite number of return words to a chosen prefix $w$ of ${\bf u}$. Ordering of the return words to $w$ in this concatenation is coded by derivated word…
We present a method for computing probability of occurence of 1s in a configuration obtained by iteration of a probabilistic cellular automata (PCA), starting from a random initial configuration. If the PCA is sufficiently simple, one can…