Related papers: Statistics for Unimodal Sequences
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…
We study sequences of partitions of a non decreasing sequence I n of intervals into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed…
For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide…
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
We consider two multiplicative statistics on the set of integer partitions: the norm of a partition, which is the product of its parts, and the supernorm of a partition, which is the product of the prime numbers $p_i$ indexed by its parts…
The use of Fermat-Torricelli points can be an effective mathematical tool for analyzing numerical series that have a large variance, a pronounced nonlinear trend, or do not have a normal distribution of a random variable. Linear…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure of concave compositions including the…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…