Related papers: On functional records and champions

The index of codivisibility of a set of integers is the size of its largest subset with a common prime divisor. For large random samples of integers, the index of codivisibility is approximately normal.

With the growing number of devices, sensors and digital systems, data logs may become uncertain due to, e.g., sensor reading inaccuracies or incorrect interpretation of readings by processing programs. At times, such uncertainties can be…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…

We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…

We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the…

The purpose of this note is to point out that the theory of expander graphs leads to an interesting test whether $n$ real numbers $x_1, \dots, x_n$ could be $n$ independent samples of a random variable. To any distinct, real numbers $x_1,…

We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…

We introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \R^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This…

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.

Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…

Given $n$ independent random marked $d$-vectors (points) $X_i$ distributed with a common density, define the measure $\nu_n=\sum_i\xi_i$, where $\xi_i$ is a measure (not necessarily a point measure) which stabilizes; this means that $\xi_i$…

It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…

Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…

In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…

With recent high-throughput technology we can synthesize large heterogeneous collections of DNA structures, and also read them all out precisely in a single procedure. Can we use these tools, not only to do things faster, but also to devise…

The names of variables and functions serve as implicit documentation and are instrumental for program comprehension. But choosing good meaningful names is hard. We perform a sequence of experiments in which a total of 334 subjects are…

We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…

Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…