Related papers: Asymptotic Enumeration of Labelled Interval Orders
In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and…
This paper deals with the state estimation of linear time-invariant systems using distributed observers with local sampled-data measurement and aperiodic communication. Each observer agent perceives partial information of the system to be…
In this paper, we shall establish a rather general asymptotic formula in short intervals for a classe of arithmetic functions and announce two applications about the distribution of divisors of square-full numbers and integers representable…
We consider lattice walks in $\R^k$ confined to the region $0<x_1<x_2...<x_k$ with fixed (but arbitrary) starting and end points. The walks are required to be "reflectable", that is, we assume that the number of paths can be counted using…
We prove asymptotic formulas for the complex coefficients of $(\zeta q;q)_\infty^{-1}$, where $\zeta$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for $p(a,b,n)$, the number of integer partitions…
We determine the number of nonequivalent chord diagrams of order $n$ under the action of two groups, $C_{2n}$, a cyclic group of order $2n$, and $D_{2n}$, a dihedral group of order $4n$. Asymptotic formulas are also established.
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
We consider the fragmentation at nodes of the L\'{e}vy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time $\theta$. This limit is increasing in…
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions…
We present a technique for reducing the order of polynomial-like iterative equations; in particular, we answer a question asked by Wenmeng Zhang and Weinian Zhang. Our method involves the asymptotic behaviour of the sequence of consecutive…
We generalize the asymptotic estimates by Bubboloni, Luca and Spiga (2012) on the number of $k$-compositions of $n$ satisfying some coprimality conditions. We substantially refine the error term concerning the number of $k$-compositions of…
In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This improves the result of Pimsert, Srichan and Tangsupphathawat (2023), the order of…
A configuration space of intervals in $\mathbb R^1$ with partially summable labels is constructed. It is a kind of an extension of the configuration space with partially summable labels constructed by the second author and at the same time…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
Let m and n be any integers with n>m>=2. Using just the entropy function it is possible to define a partial order on S_mn (the symmetric group on mn letters) modulo a subgroup isomorphic to S_m x S_n. We explore this partial order in the…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the…
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the…