We propose explicit expressions for the form factors, including their normalization constants, of topologically charged (or soliton-creating) operators in the sine-Gordon model. The normalization constants, which constitute the main content of our proposal, allow one to find exact relations between the shortand long-distance asymptotics of the correlation functions. We make predictions concerni...

Small perturbations of the Jacobi matrix with weights √ n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh formula for the Schrödinger operator on the half-line with summable potential. Additionally a base of generalized eigenvectors for ”free” Hermite ope...

In a previous study logarithmic large-buffer asymptotics were derived for a two-class generalized processor sharing system with Gaussian inputs, for three of the four possible scenarios. In this note we show how the large-buffer asymptotics for the remaining fourth regime follow from a recently derived result for tandem systems. We also provide a heuristic interpretation of the result. 2000 Mat...

The number of comparisons Xn used by Quicksort to sort an array of n distinct numbers has mean μn of order n log n and standard deviation of order n. Using different methods, Régnier and Rösler each showed that the normalized variate Yn := (Xn−μn)/n converges in distribution, say to Y ; the distribution of Y can be characterized as the unique fixed point with zero mean of a certain distribution...

We review the present status of the null cone approach to numerical evolution being developed by the Pittsburgh group. We describe the simplicity of the underlying algorithm as it applies to the global description of general relativistic spacetimes. We also demonstrate its effectiveness in revealing asymptotic physical properties of black hole formation in the gravitational collapse of a scalar...

Abstract. This is a continuation of the papers [4] of Bleher and Fokin and [6] of Bleher and Liechty, in which the large n asymptotics is obtained for the partition function Zn of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large n asymptotics of Zn on the critical line between these two p...

It is shown that the following conditions are equivalent for the generalized Schur class functions w at a boundary point t0 ∈ T: Carathéodory– Julia type condition of order n ([2], [3]); agreeing of asymptotics from inside and outside of the disk D up to order 2n+1 ([11]); t0-isometry of the coefficients of the boundary asymptotics; a certain structured matrix P constructed from these coefficie...

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ρ = 0. We also compute large-time asymptotics for the CEV model in the largetime, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao&Lee[GL...

We establish the asymptotic expansion of certain integrals of ψ classes on moduli spaces of curves Mg,n when either the g or n goes to infinity. Our main tools are cut-join type recursion formulae from the WittenKontsevich theorem as well as asymptotics of solutions to the first Painlevé equation. We also raise a conjecture on large genus asymptotics for n-point functions of ψ classes and parti...

Let Fn(x) be the partition polynomial ∑k=1 pk(n)x where pk(n) is the number of partitions of n with k parts. We emphasize the computational experiments using degrees up to 70,000 to discover the asymptotics of these polynomials. Surprisingly, the asymptotics of Fn(x) have two scales of orders n and √ n and in three different regimes inside the unit disk. Consequently, the zeros converge to netw...