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Universality in blow-up for nonlinear heat equations
We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer k, weExpand
Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations
We present a general method for studying long-time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. ItExpand
Chance in physics : foundations and perspectives
Bayes, Boltzmann and Bohm: Probabilities in Physics.- Classical Statistical Mechanics.- The Rise of Statistical Mechanics.- Boltzmann's Approach to Statistical Mechanics.- Microscopic TimeExpand
I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to LaplaceExpand
Percolation in strongly correlated systems: The massless Gaussian field
We derive a number of new results for correlated nearest neighbor site percolation onZd. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., theExpand
High temperature expansions and dynamical systems
We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of theExpand
Random walks in asymmetric random environments
We consider random walks on Zd with transition ratesp(x, y) given by a random matrix. Ifp is a small random perturbation of the simple random walk, we show that the walk remains diffusive for almostExpand
Phase transition in the 3d random field Ising model
We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,dl for the theory isdl≦2, settlingExpand
Making Sense of Quantum Mechanics
This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannotExpand