Limit process of stationary TASEP near the characteristic line

Baik, Jinho; Ferrari, Patrik L.; Péché, Sandrine

doi:10.1002/cpa.20316

Cited by 100 publications

(195 citation statements)

References 32 publications

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“…• One pt: F GUE [9,93] • Multi pt: Airy 2 [137,94,29] • One pt: F 0 [11,69] • Multi pt: Airy stat [10] • One pt: F GOE [12,13,70,146] • Multi pt: Airy 1 [31,32] • One pt: (F GOE ) 2 [11,8,136,19] • Multi pt: Airy 2→BM [90,46] • Multi pt: Airy 2→1 [33] • Multi pt: Airy 1→BM [34] KPZ/SHE…”

Section: Fluctuationsmentioning

confidence: 99%

“…There is, in fact, a scaling window for the critical tuning and within that window one introduces a drift into the two sides of the Brownian motion B(X). The long time scaling behavior of this whole window is understood (in terms of last passage percolation) in [35,10,46]. • Z(0, X) = 1: (1) Point to line polymer; (2) Limit of polymers which go from a fixed point and terminate at a fixed time n (without a fixed endpoint); (3) Limit when boundary conditions are deterministic and critically tuned.…”

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

The Kardar–parisi–zhang Equation and Universality Class

Corwin

2012

Random Matrices: Theory Appl.

722

824

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Abstract. Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past twenty five years a new universality class has emerged to describe a host of important physical and probabilistic models (including one dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar-Parisi-Zhang (KPZ) universality class and underlying it is, again, a continuum object -a non-linear stochastic partial differential equation -known as the KPZ equation.The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media.As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

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Section: Fluctuationsmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

The Kardar–parisi–zhang Equation and Universality Class

Corwin

2012

Random Matrices: Theory Appl.

722

824

View full text Add to dashboard Cite

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“…The mode-coupling equation takes the form 19) which is the one-loop approximation for the stochastic Burgers equation [39] . For large x, t, its solution with initial condition f (x, 0) = δ(x) takes the scaling form…”

Section: Mode-coupling Theorymentioning

confidence: 99%

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Spohn

2016

Thermal Transport in Low Dimensions

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Abstract. Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to develop a nonlinear extension of fluctuating hydrodynamics. The relevant nonlinearity turns out to be the quadratic part of the Euler currents when expanding relative to a uniform background. We outline the theory and compare with recent molecular dynamics simulations. 1 arXiv:1505.05987v2 [cond-mat.stat-mech]

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“…We refer the reader to the corresponding references for more details on the differences. In the case of multipoint results, one can translate between the various settings by using the slow decorrelation result proved of [Fer08;CFP12], as done in [BFP10;CFP10].…”

Section: Tracy-widom Distributionsmentioning

confidence: 99%

“…Its definition is also given in terms of finite-dimensional distributions involving Fredholm determinants, but the formulas are a lot more cumbersome. We will not need the exact formulas, so we refer the reader to [BFP10] for the details. Despite its name, A stat is not stationary as a process.…”

Section: Tracy-widom Distributionsmentioning

confidence: 99%

Airy Processes and Variational Problems

Quastel

Remenik

2014

Topics in Percolative and Disordered Systems

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Abstract. We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.

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Limit process of stationary TASEP near the characteristic line

Cited by 100 publications

References 32 publications

The Kardar–parisi–zhang Equation and Universality Class

The Kardar–parisi–zhang Equation and Universality Class

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Airy Processes and Variational Problems

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