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 Laplaceâ€¦ (More)

We present a general method for studying long time asymptotics of nonlin-ear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. Itâ€¦ (More)

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 theâ€¦ (More)

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 blowup point, and for each integer k, weâ€¦ (More)

We present some results on the shape and size of the percolative region of the nearest neighbor ferromagnetic Ising model on yd. The percolat ion properties of the connected clusters of (say) the +â€¦ (More)

We study the initial value problem of the thermal-diffusive combustion system: u1,t = u1,x,xâˆ’u1u2, u2,t = du2,xx+u1u2, x âˆˆ R1, for non-negative spatially decaying initial data of arbitrary size andâ€¦ (More)

We generalize the notion of "ground states" in the Pirogov-Sinai theory of first order phase transitions at low temperatures, applicable to lattice systems with a finite number of periodic groundâ€¦ (More)

We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these innnite dimensional dynamicalâ€¦ (More)

We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure hasâ€¦ (More)

We explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples ofâ€¦ (More)