Almost-Sure Central Limit Theorem for Directed Polymers and Random Corrections

We consider a general model of directed polymers on the lattice , weakly coupled to a random environment. We prove that the central limit theorem holds almost surely for the discrete time random walk X _T associated to the polymer. Moreover we show that the random corrections to the cumulants of X _T are finite, starting from some dimension depending on the index of the cumulants, and that there are corresponding random corrections of order , , in the asymptotic expansion of the expectations of smooth functions of X _T . Full proofs are carried out for the first two cumulants. We finally prove a kind of local theorem showing that the ratio of the probabilities of the events to the corresponding probabilities with no randomness, in the region of “moderate” deviations from the average drift bT, are, for almost all choices of the environment, uniformly close, as , to a functional of the environment “as seen from (T,y)$”. Received: 14 October 1996 / Accepted: 28 March 1997     

Diffusive behavior of asymmetric zero-range processes

We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

Relativistic quantum defect calculations on the copper isoelectronic sequence

The quantum defect orbital (QDO ) method and its relativistic (RQDO ) counterpart have been employed in this work to compute oscillator strengths for several fine-structure transitions in members of the copper isoelectronic sequence up to Z = 92. The RQDO results are found to be in quite good agreement with the best estimates derived from other sources, whenever the comparison is possible. © 1994 John Wiley & Sons, Inc.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.