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Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures
Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν are considered, both of which are assumed to have a translation-invariant finite-range interaction.
Duality and Hidden Symmetries in Interacting Particle Systems
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in…
On the definition of entropy production, via examples
This work presents a definition of entropy production rate for classes of deterministic and stochastic dynamics, motivated by recent work on the Gallavotti–Cohen (local) fluctuation theorem.
Concentration inequalities for random fields via coupling
A new and simple approach to concentration inequalities in the context of dependent random processes and random fields based on coupling that applies to Gibbs random fields, both at high and low temperatures.
Mathematical aspects of the abelian sandpile model
- F. Redig
In 1988, Bak, Tang and Wiesenfeld (BTW) introduced a lattice model of what they called “self-organized criticality”. Since its appearance, this model has been studied intensively, both in the physics…
Almost Gibbsian versus weakly Gibbsian measures
The Abelian sandpile : a mathematical introduction
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find…
Law of Large Numbers for a Class of Random Walks in Dynamic Random Environments
In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on…
Limiting Shapes for Deterministic Centrally Seeded Growth Models
Abstract We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤd, Levine and Peres proved that the limiting shape of the growth cluster is a sphere.…
Intermittency and weak Gibbs states
We show that the natural invariant state for Manneville-Pomeau maps can be characterized as a weakly Gibbsian state. In this way we make a connection between the study of intermittency via…