Random Walk on Nonnegative Integers in Beta Distributed Random Environment

Barraquand, Guillaume; Rychnovsky, Mark

doi:10.1007/s00220-022-04536-1

Cited by 6 publications

(2 citation statements)

References 43 publications

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“…Beyond just the phase transition studied in this paper, there has been tremendous progress in understanding half‐space models at positive temperature and their algebraic structure, see, for example, [9, 12, 13, 22, 32, 43, 44]. For some additional recent works on half‐space models, see [6, 16, 19, 33, 34, 47], and also relevant work in the physics literature [10, 11, 17].…”

Section: Introductionmentioning

confidence: 99%

Boundary current fluctuations for the half‐space ASEP and six‐vertex model

2024

Proceedings of London Math Soc

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We study fluctuations of the current at the boundary for the half‐space asymmetric simple exclusion process (ASEP) and the height function of the half‐space six‐vertex model at the boundary at large times. We establish a phase transition depending on the effective density of particles at the boundary, with Gaussian symplectic ensemble (GSE) and Gaussian orthogonal ensemble (GOE) limits as well as the Baik–Rains crossover distribution near the critical point. This was previously known for half‐space last‐passage percolation, and recently established for the half‐space log‐gamma polymer and Kardar–Parisi–Zhang equation in the groundbreaking work of Imamura, Mucciconi, and Sasamoto. The proof uses the underlying algebraic structure of these models in a crucial way to obtain exact formulas. In particular, we show a relationship between the half‐space six‐vertex model and a half‐space Hall–Littlewood measure with two boundary parameters, which is then matched to a free boundary Schur process via a new identity of symmetric functions. Fredholm Pfaffian formulas are established for the half‐space ASEP and six‐vertex model, indicating a hidden free fermionic structure.

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Section: Introductionmentioning

confidence: 99%

Boundary current fluctuations for the half‐space ASEP and six‐vertex model

2024

Proceedings of London Math Soc

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“…Since the early work by Kardar [Kar85], the half-space KPZ equation has received significant attention, with a flurry of new results recently in in both mathematics [CS18, BBCW18, BBC20, Par19, Par22, BC23, IMS22] and physics literature [GLD12, BBC16, IT18, DNKLDT20, KLD18, BKLD20, BLD21, BKLD22]. Apart from log-gamma and continuum polymer, a half-space version of the beta polymer was recently introduced and studied in [BR22].…”

Section: Introductionmentioning

confidence: 99%

An Identity in Distribution Between Full-Space and Half-Space Log-Gamma Polymers

Barraquand

Wang

2022

International Mathematics Research Notices

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We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant and (2) the point-to-line partition function in an octant. As an application, we prove that the point-to-line free energy of the log-gamma polymer in an octant obeys a phase transition depending on the strength of the noise along the boundary. This transition of (de)pinning by randomness was first predicted in physics by Kardar in 1985 and proved rigorously for zero temperature models by Baik and Rains in 2001. While it is expected to arise universally for models in the Kardar–Parisi–Zhang universality class, this is the first positive temperature model for which this transition can be rigorously established.

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Crossover from the macroscopic fluctuation theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion

Krajenbrink¹,

Doussal

2023

Phys. Rev. E

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Random Walk on Nonnegative Integers in Beta Distributed Random Environment

Cited by 6 publications

References 43 publications

Boundary current fluctuations for the half‐space ASEP and six‐vertex model

Boundary current fluctuations for the half‐space ASEP and six‐vertex model

An Identity in Distribution Between Full-Space and Half-Space Log-Gamma Polymers

Crossover from the macroscopic fluctuation theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion

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