A pedestrian's view on interacting particle systems, KPZ universality and random matrices
By Thomas Kriecherbauer, Joachim Krug. 2008
240 citations recorded by the source corpus.
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar–Parisi–Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson [59] that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy–Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c71e9a298e10023f19f11b5af529444a4bf91593
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Citations in the corpus
- An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “ly evolving field around the KPZ class. It is not a review of recent mathematical approaches nor a technical guide to solve the problems, for which the readers are referred to more appropriate reviews [14, 15, 17, 18] and references therein. Instead, it is intended to provide useful information for n”
- Random Quantum Circuits (2022, background): “χy,t is a random variable, of order 1 size, that depends on the realization (157, 158, 159).”
- Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence (2012, background): “Surprisingly, the derived distribution function depends on whether the interfaces are initially flat or curved [19, 49, 71, 72, 83] but is nevertheless expected to be universal.”
- The Kardar-Parisi-Zhang equation and universality class (2011, background): “A number of books and review articles have been written about these models in mathematics and physics, including [18, 44, 82, 86, 100, 102, 106, 108, 115, 117, 120, 158, 157].”
- Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, background): “Information about this fixed point has generally come from studying exactly 2More precisely, the uniqueness should be up to a space-time scaling by parameters which can be calculated from the microscopic properties of the polymer such as dP0, β and the disorder distribution (see, for example, [46, 5”
- Emergent statistical mechanics of entanglement in random unitary circuits (2018, unknown): “[78] Thomas Kriecherbauer and Joachim Krug.”
- Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, unknown): “for F2(s) can be found, for example, in [182].”