Large time asymptotics of growth models on space-like paths I: PushASEP

By Alexei Borodin, Patrik L. Ferrari Caltech, Wias Berlin. 2007

166 citations recorded by the source corpus.

We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of theheight function of the associated growth model along any space-like path are described by the Airy 1 and Airy 2 processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c9eb85a9e08c3f8ed65b2245cd0057d994596489

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions (2010, methodology): “,m} and whereA2 is the Airy2 process (see, for example, [7, 11]) and has one-point marginals FGUE.”
The Kardar-Parisi-Zhang equation and universality class (2011, unknown): “2 h¯(T,TX) = T/2 ¯h(T,TX) = −X X<−1 T1+X2 2 X∈[−1,0] T/2 X>0 h¯(T,TX) = −X X<−1 T1+X2 2 X∈[−1,0] T/2 X>0 h¯(T,TX) = T/2 Fluctuations •One pt: FGUE [9, 93] •Multi pt: Airy2 [137, 94, 29] •One pt: F0 [11, 69] •Multi pt: Airystat [10] •One pt: FGOE [12, 13, 70, 146] •Multi pt: Airy1 [”
The directed landscape (2018, background): “any space-like curve converge uniformly to an Airy process. Previous approaches to such results include ﬁnding speciﬁc determinantal formulas for space-like curves (i.e. Borodin and Olshanski (2006), Borodin and Ferrari (2008)) and geometric analysis of slow decorrelations (i.e. Ferrari (2008), Corw”
Height Fluctuations for the Stationary KPZ Equation (2014, result): “esses forthese models were determined. These statistical properties agreed between the models, but depended non-trivially on the type of initial data or geometry for the growth models, such as curved [6,10,21,22,60,61,68], ﬂat [10,21,23–25,43,48,73] or stationary [7–9,47,49,57,69]. All these results”
Lectures on integrable probability (2012, methodology): “t particlesby one, seeFigure18for anillustration oftheserules. Thedynamics wehave just described is known as the Long Range Totally Asymmetric Exclusion Process, and itisalsoaspecialcaseofPushASEP,see[Borodin-Ferrari-08a],[Spitzer-70]. Figure18: PushASEP.Toppanel: jumpofaparticle. Bottompanel: jumpo”
Determinantal point processes (2018, methodology): “nel can be written in the form K(tn1 a1,x1;t n2 a2,x2) = −φ (tn2 a2,t n1 a1)(x2,x1) + Xn1 i=1 XN j=1 G−t ij (φi ∗ φ (ti c(i) ,t n1 a1))(virt,x 1)Ψ t 2 a2 j (x2). One proof of Theorem 4.4 was given in [Bor08b]; another proof can be found in Section 4.4 of [For08]. Although we stated Theorem 4.4 for t”