arXiv subjects

Frank Redig

Publications and source records attributed to Frank Redig.

77 records · Page 5Linked to original sources

arXiv2001

Variational principle and almost quasilocality for some renormalized measures

We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We first point out that a recent theory due to Pfister implies that for block-transformed measures free energies and relative entropy densities exist and are conjugate convex functionals. We then determine a necessary and sufficient condition for consistency with a specification that is quasilocal in a fixed direction. As corollaries we obtain consistency results for models with FKG monotonicity and for models with appropriate "continuity rates". For (noisy) decimations or projections of the Ising model, these results imply almost quasilocality of the decimated "+" and "-" measures.

math.PR↗

arXiv2001

From Global to Local Fluctuation Theorems

The Gallavotti-Cohen fluctuation theorem suggests a general symmetry in the fluctuations of the entropy production, a basic concept in the theory of irreversible processes, based on results in the theory of strongly chaotic maps. We study this symmetry for some standard models of nonequilibrium steady states. We give a general strategy to derive a 'local' fluctuation theorem exploiting the Gibbsian features of the stationary space-time distribution. This is applied to spin flip processes and to the asymmetric exclusion process.

cond-mat.stat-mech↗

arXiv2001

The Abelian Sandpile Model on an Infinite Tree

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality.

math-ph↗

arXiv2000

On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid

We model the behavior of a big (Brazil) nut in a medium of smaller nuts with a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice system. The polymer or `rod' can move up or down in an external negative field, occupying N horizontal lattice sites where the monomers cannot enter. The monomers (at most one per site) or `fluid particles' are moving symmetrically in the horizontal plane and asymmetrically in the vertical direction, also with a negative field. For a fixed position of the rod, this lattice fluid is in equilibrium with a vertical height profile reversible for the monomers' motion. Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically decouples from that of the monomers resulting in a reversible random walk for the rod around an average height proportional to log N.

math.PR↗

arXiv1999

Stretched Exponential Relaxation in the Biased Random Voter Model

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+α)$, where $0<α\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).

math-ph↗