Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model

Korotkikh, Sergei

doi:10.1007/s00440-022-01117-0

Cited by 5 publications

(3 citation statements)

References 70 publications

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“…work of Borodin and Wheeler [23]), shift invariance in the generality considered in this paper was first formulated and established by Borodin, Gorin, and Wheeler [22], who proved it for the stochastic six vertex model, and obtained results for other models including certain polymer models and the KPZ equation through various limits and specializations. Subsequently, these results were extended to other models and generalized [28,32,37,40]. They have already found some applications, see [25,54].…”

Section: Introductionmentioning

confidence: 80%

Shift invariance of half space integrable models

He¹

2022

Preprint

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We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type B analogue of the oriented swap process and last passage times in a half space, establishing the Baik-Ben Arous-Péché phase transition for the absorption time. The proof uses Hecke algebras and integrability of the six vertex model through the Yang-Baxter and reflection equations.

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Section: Introductionmentioning

confidence: 80%

Shift invariance of half space integrable models

He¹

2022

Preprint

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“…An integrable vertex model (which is not determinantal) with three parameter sequences has recently been studied in[93]. Whether this model has a free fermion version, which presumably would give a TASEP-like model with three sequences of parameters, and whether this would be related to any of the inhomogeneous models of the present paper is an interesting question 5.…”

mentioning

confidence: 83%

Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays

Assiotis

2020

Ann. Henri Poincaré

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We introduce a space inhomogeneous generalization of the dynamics on interlacing arrays considered by Borodin and Ferrari in [7]. We show that for a certain class of initial conditions the point process associated to the dynamics has determinantal correlation functions and we calculate explicitly, in the form of a double contour integral, the correlation kernel for one of the most classical initial conditions, the densely packed. En route to proving this we obtain some results of independent interest on non-intersecting general pure-birth chains, that generalize the Charlier process, the discrete analogue of Dyson's Brownian motion. Finally, these dynamics provide a coupling between the inhomogeneous versions of the TAZRP and PushTASEP particle systems which appear as projections on the left and right edges of the array respectively⋆ ⋆ + 1 ⋆ + 2 ⋆ + 3 ⋆ + 4 ⋆ + 5 ⋆ + 6 Figure 1: A configuration of particles in GT 4 . If the clock of the particle labelled X 3,1 4 rings, which happens at rate λ(⋆ + 1), then the move is blocked since interlacing with X 2,1 4 would be violated. On the other hand, if the clock of the particle X 2,2 4 rings, which happens at rate λ(⋆ + 3), then it jumps to the right by one and instantaneously pushes both X 3,3 4 and X 4,4 4 to the right by one as well, for otherwise the interlacing would break.The right edge particle system is called inhomogeneous PushTASEP, see [7], [6] and also [16] for a q-deformation of the homogeneous case. The fact that this particle system has an underlying determinantal structure is new as well, but is also obtained in the independent work of Petrov [46] that uses different methods.

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“…This was brought into focus in [61] which discovered that in this scale the Tracy-Widom GUE distribution is replaced by that of the KPZ equation [62][63][64][65][66] confirming some predictions of [60]. See [67][68][69][70][71][72][73] for further developments. The occurrence of the KPZ equation / universality class in the large deviations for RWREs was unexpected and is useful as the statistics associated to these objects are well studied theoretically and numerically.…”

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confidence: 89%

Anomalous Fluctuations of Extremes in Many-Particle Diffusion

Hass¹,

Carroll-Godfrey²,

Corwin³

et al. 2022

Preprint

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In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of Einstein's treatment of single-particle diffusion, has each particle taking independent homogeneous random walks. This, however, neglects the fact that all particles diffuse in a common and often inhomogeneous environment that can affect their motion. A more sophisticated model treats this common environment as a space-time random biasing field which influences each particle's independent motion. While the bulk (or typical particle) behavior of these two models has been found to match to high degree, recent theoretical work of Barraquand, Corwin and Le Doussal on a one-dimensional exactly solvable version of this random environment model suggests that the extreme behavior is quite different between the two models. We transform these asymptotic (in system size and time) results into physically applicable predictions. Using high precision numerical simulations we reconcile different asymptotic phases in a manner that matches numerics down to realistic system sizes, amenable to experimental confirmation. We characterize the behavior of extreme diffusion in the random environment model by the presence of a new phase with anomalous fluctuations related to the Kardar-Parisi-Zhang universality class and equation.

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Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model

Cited by 5 publications

References 70 publications

Shift invariance of half space integrable models

Shift invariance of half space integrable models

Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays

Anomalous Fluctuations of Extremes in Many-Particle Diffusion

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