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We review a (constructive) approach first introduced in [6] and further developed in [7, 8, 38, 9] for hydrodynamic limits of asymmetric attractive particle systems, in a weak or in a strong (that is, almost sure) sense, in an homogeneous or in a quenched disordered setting.
We prove quenched hydrodynamic limit under hyperbolic time scaling for bounded attractive particle systems on $Z$ in random ergodic environment. Our result is a strong law of large numbers, that we illustrate with various examples.
We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $Z$ starting from an arbitrary initial profile. We generalize earlier works by Seppalainen (1999) and Andjel et al. (2004). Our constructive approach require
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature
Let $R$ be the power series ring or the polynomial ring over a field $k$ and let $I $ be an ideal of $R.$ Macaulay proved that the Artinian Gorenstein $k$-algebras $R/I$ are in one-to-one correspondence with the cyclic $R$-submodules of the divided p
We study the approach to equilibrium of the event-chain Monte Carlo (ECMC) algorithm for the one-dimensional hard-sphere model. Using the connection to the coupon-collector problem, we prove that a specific version of this local irreversible Markov c