Related papers: On the evolution of random integer compositions
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
Prime numbers appeared in contexts spanning statistical mechanics, quantum mechanics and dynamical systems. However, the mechanisms governing the irregularities observed in their sequence and linking them to physical systems remained…
Let $\{U_n\}_{n \geqslant 0}$ and $\{G_m\}_{m \geqslant 0}$ be two linear recurrence sequences defined over the integers. We establish an asymptotic formula for the number of integers $c$ in the range $[-x, x]$ which can be represented as…
For a fixed integer base $b\geq2$, we consider the number of compositions of $1$ into a given number of powers of $b$ and, related, the maximum number of representations a positive integer can have as an ordered sum of powers of $b$. We…
We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
The entropy of the random walk on the discrete contable group could be used for comparison of the system of the generators. Fundamental inequality between growth, entropy and escape gives the possibility to define "the best" system of the…
Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a randomly generated one is concerned, an attractive question…
This paper presents two alternative approaches for counting the number of two-row weakly increasing matrices, which are $2\times n$ matrices whose entries are integers from $1$ to $k$ and are weakly increasing along all rows and columns,…
The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current…
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
Growing Neutrino quintessence describes a form of dynamical dark energy that could explain why dark energy dominates the universe only in recent cosmological times. This scenario predicts the formation of large scale neutrino lumps which…
Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear…
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…
Recently, a supersymmetric model of dark energy coupled to cold dark matter, the supersymmetron, has been proposed. In the absence of cold dark matter, the supersymmetron field converges to a supersymmetric minimum with a vanishing…
A famous result by Hammersley and Versik-Kerov states that the length $L_n$ of the longest increasing subsequence among $n$ iid continuous random variables grows like $2\sqrt{n}$. We investigate here the asymptotic behavior of $L_n$ for…
We consider a set $\mbK = \bigcup_{n \in \mbbN}\mbK_n$ of {\em finite} structures such that all members of $\mbK_n$ have the same universe, the cardinality of which approaches $\infty$ as $n\to\infty$. Each structure in $\mbK$ may have a…