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Sergei K. Nechaev 1 The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice using the Kauffman algebraic invariants and show the connection of this problem with the thermodynamic properties of 2D […]

P. Leboeuf 1, G. Iacomelli The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit the return amplitude to the initial state and the transition amplitude to any other

Saxena, A., S., Brazovskii, N., Kirova, Z.G., Yu, A.R., Bishop Synthetic Metals 101 (1999) 325-326

E. B. Bogomolny 1, D. C. Rouben 1 European Physical Journal B 9 (1999) 695-718 We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field

J. Houdayer 1, O. C. Martin 1 Physical Review Letters 83 (1999) 1030-1033 The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and

Pierre Le Doussal 1, Cecile Monthus 2, 3 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 60 (1999) 1212-1238 We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai

Daniel S. Fisher 1, Pierre Le Doussal 2, Cecile Monthus 3 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 59 (1999) 4795 Sinai\’s model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We

P. Leboeuf 1 Journal of Statistical Physics 95 (1999) 651-664 The statistical properties of random analytic functions psi(z) are investigated as a phase-space model for eigenfunctions of fully chaotic systems. We generalize to the plane and to the hyperbolic plane a theorem concerning the equidistribution of the zeros of psi(z) previously demonstrated for a spherical phase space

Brazovskii, S., Kirova, N. Synthetic Metals103 (1999) 2589-2592

Brazovskii, S., Kirova, N., Smilgies, D., Grubel, G. Physica B280 (1999) 317