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In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusBrownian Aspects of the KPZ Fixed Point

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Brownian Aspects of the KPZ Fixed... [The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the local space regularity and the long time evolution. Most of the results that we will present here were obtained by either applying explicit formulas for the transition probabilities or applying the coupling method to discrete approximations. Instead we will use the variational description of the KPZ fixed point, allowing us the possibility of running the process starting from different initial data (basic coupling), to prove directly the aforementioned limiting behaviours.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusBrownian Aspects of the KPZ Fixed Point

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.

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References (28)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
711 –739
DOI
10.1007/978-3-030-60754-8_29
Publisher site
See Chapter on Publisher Site

Abstract

[The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the local space regularity and the long time evolution. Most of the results that we will present here were obtained by either applying explicit formulas for the transition probabilities or applying the coupling method to discrete approximations. Instead we will use the variational description of the KPZ fixed point, allowing us the possibility of running the process starting from different initial data (basic coupling), to prove directly the aforementioned limiting behaviours.]

Published: Nov 4, 2020

Keywords: Random growth; Kardar-Parisi-Zhang fixed point; Brownian motion

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