Related papers: Range-Renewal Structure of I.I.D. Samplings
This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…
Theory of Kingman's partition structures has two culminating points: the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, known as Kingman's paintbox; a…
Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's…
We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
We describe and analyze a simple random feature scheme (RFS) from prescribed compositional kernels. The compositional kernels we use are inspired by the structure of convolutional neural networks and kernels. The resulting scheme yields…
A common and effective method for calculating the steady-state distribution of a process under stochastic resetting is the renewal approach that requires only the knowledge of the reset-free propagator of the underlying process and the…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative property, the convergence in distribution for the recurrence…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Consider multiple sums $S_n$ on the $d$-dimensional integer grid,which are generated by i.i.d.\ random variables with a positive expectation. We prove the strong law of large numbers, the law of the iterated logarithm and the distributional…
Dealing with compound renewal process with generally distributed jump sizes and inter-renewal intervals, we focus on the approximation for the fixed-probability level, which is the core of inverse level crossing problem. We are developing…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…
In this article we discuss a relation between the string topology and differential forms based on the theory of Chen's iterated integrals and the cyclic bar complex.