On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

A strong limit theorem for generalized Cantor-like random sequences

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The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations theory are consistent (in a certain sense) with the result using dominant pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the cell loss ratio, an important performance measure for service systems such as ATM networks. The analysis relies on a new generalization of the Taylor coefficients of a complex function which we call characteristic coefficients. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate multiclass M/D/n system.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Characterization of distribution of pi-electrons amongst benzenoid rings for Randić’s “algebraic” Kekulé structures

For benzenoid hydrocarbons the distribution of pi-electrons amongst rings is characterized in the context of Randis mode of assignment attending to the different Kekulé structures. In particular the mean and mean deviation from the mean are considered, and the benzenoids which achieve maximum deviation are identified.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

Consequences of the ‘Pedersen papers’ on crown type chemistry at Würzburg and Bonn Universities: From heteroaromatic crowns and podands to large molecular and crystalline cavities including multisite receptors,cascade molecules,chromoionophores, siderophores,surfactant-type,and extreme ligands

We thank the editors of this issue for the opportunity to present the historic development of crown chemistry at the Universities of Wurzburg and Bonn in memory of C. J. Pedersen, the originator of the crown ethers. His legacy of science has tremendously stimulated research at both universities.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

Spectral density distribution moments of a Hamiltonian of N coupled Morse oscillators: The large‐N limit

The expressions for moments of spectral density distribution of a Hamiltonian representing a system of N coupled Morse oscillators are reduced to the large‐N limit. The effect of the values of coupling constants on the spectral density distribution is analyzed. For the values of coupling constants within the pertinent range for real molecules, the relations between moments appear to be close to those for a Gaussian distribution. Outside this range, the deviations from the normal distribution are substantial. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002