Coulomb-Gas Electrostatics Controls Large Fluctuations of the Kardar-Parisi-Zhang Equation

Physical Review Letters
Ivan CorwinLi-Cheng Tsai

Abstract

We establish a large deviation principle for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition. Our analysis exploits an exact connection between the KPZ one-point distribution and the Airy point process-an infinite particle Coulomb gas that arises at the spectral edge in random matrix theory. We develop the large deviation principle for the Airy point process and use it to compute, in a straightforward and assumption-free manner, the KPZ large deviation rate function in terms of an electrostatic problem (whose solution we evaluate). This method also applies to the half-space KPZ equation, showing that its rate function is half of the full-space rate function. In addition to these long-time estimates, we provide rigorous proof of finite-time tail bounds on the KPZ distribution, which demonstrate a crossover between exponential decay with exponent 3 (in the shallow left tail) to exponent 5/2 (in the deep left tail). The full-space KPZ rate function agrees with the one computed in Sasorov et al. [J. Stat. Mech. (2017) 063203JSMTC61742-546810.1088/1742-5468/aa73f8] via a WKB approximation analysis of a nonlocal, nonlinear integrodiffer...Continue Reading

References

Dec 23, 1985·Physical Review Letters·D A HuseD S Fisher
Mar 3, 1986·Physical Review Letters·M KardarY C Zhang
May 18, 1987·Physical Review Letters·M Kardar, Y C Zhang
Dec 13, 2006·Physical Review Letters·David S Dean, Satya N Majumdar
Oct 13, 2007·Physical Review Letters·A M SomozaJ Prior
Dec 7, 2007·Proceedings of the National Academy of Sciences of the United States of America·Oskar HallatschekDavid R Nelson
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David S Dean, Satya N Majumdar
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I V Kolokolov, S E Korshunov
Sep 28, 2010·Physical Review Letters·Kazumasa A Takeuchi, Masaki Sano
Sep 28, 2010·Physical Review Letters·Tomohiro Sasamoto, Herbert Spohn
Jul 21, 2011·Physical Review Letters·Pasquale Calabrese, Pierre Le Doussal
Feb 23, 2012·Scientific Reports·Kazumasa A TakeuchiHerbert Spohn
Sep 26, 2012·Physical Review Letters·Takashi Imamura, Tomohiro Sasamoto
Apr 4, 2015·Physical Review Letters·David S DeanGrégory Schehr
Jul 22, 2015·Physical Review Letters·Séverine AtisKay Jörg Wiese
Mar 5, 2016·Physical Review Letters·Baruch MeersonArkady Vilenkin
Sep 13, 2016·Scientific Reports·Indu Gupta, Bhaskar Chandra Mohanty
Jan 20, 2018·Physical Review. E·Pierre Le Doussal, Thimothée Thiery
Jun 17, 2018·Physical Review. E·Naftali R Smith, Baruch Meerson

❮ Previous
Next ❯

Citations

Sep 20, 2018·Physical Review Letters·Daniel Nickelsen, Hugo Touchette
Aug 24, 2021·Physical Review Letters·Alexandre Krajenbrink, Pierre Le Doussal

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.