Related papers: Thresholds for patterns in random permutations wit…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.
We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…
This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
We count the number of occurrences of restricted patterns of length 3 in permutations with respect to length and the number of cycles. The main tool is a bijection between permutations in standard cycle form and weighted Motzkin paths.
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
A general characterization of lower and upper threshold configurations for two particle reactions is determined under the assumptions that the single particle dispersion relations E(p) are rotationally invariant and monotonic in p, and that…
Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,...,n\}$ with cycle lengths belonging to $A$. Furthermore, let $\mid A(n)\mid$ denote the cardinality of the set $A(n)=A\cap [n]$. The limit…
We study occurrences of patterns on clusters of size n in random fields on Z^d. We prove that for a given pattern, there is a constant a>0 such that the probability that this pattern occurs at most an times on a cluster of size n is…
In this paper, we propose a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. Our approach involves introducing the concept of a…
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
A permutation P on {1,..,N} is a_fast_forward_permutation_ if for each m the computational complexity of evaluating P^m(x)$ is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions.…
During the last few years, several studies have proposed the existence of a threshold separating classical from quantum behavior of objects that is dependent on the size and mass of an object as well as being dependent on certain properties…
We investigate permutations and involutions that avoid a pattern of length three and have a {\em unique} longest increasing subsequence.
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…