# HALF-SPACE MACDONALD PROCESSES

@article{Barraquand2020HALFSPACEMP, title={HALF-SPACE MACDONALD PROCESSES}, author={Guillaume Barraquand and Alexei Borodin and Ivan Corwin}, journal={Forum of Mathematics, Pi}, year={2020}, volume={8} }

Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems, including the Kardar–Parisi–Zhang (KPZ) equation and a number of other models in its universality class. In this paper, we develop the structural theory behind half-space variants of these models and the corresponding half-space Macdonald processes. These…

## 26 Citations

Free field approach to the Macdonald process

- MathematicsJournal of Algebraic Combinatorics
- 2020

The Macdonald process is a stochastic process on the collection of partitions that is a $(q,t)$-deformed generalization of the Schur process. In this paper, we approach the Macdonald process…

Stationary measures for the log-gamma polymer and KPZ equation in half-space

- Mathematics
- 2022

. We construct explicit one-parameter families of stationary measures for the Kardar-Parisi-Zhang equation in half-space with Neumann boundary conditions at the origin, as well as for the log-gamma…

Positive random walks and an identity for half-space SPDEs

- MathematicsElectronic Journal of Probability
- 2022

The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet…

Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field

- Mathematics
- 2021

Abstract. Stable spin Hall-Littlewood symmetric polynomials labeled by partitions were recently introduced by Borodin and Wheeler in the context of higher spin six vertex models, which are…

Shift invariance of half space integrable models

- Mathematics
- 2022

. 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…

Stationary Half-Space Last Passage Percolation

- MathematicsCommunications in Mathematical Physics
- 2020

In this paper we study stationary last passage percolation with exponential weights and in half-space geometry. We determine the limiting distribution of the last passage time in a critical window…

The geometric Burge correspondence and the partition function of polymer replicas

- MathematicsSelecta Mathematica
- 2021

We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric…

Random walk on nonnegative integers in beta distributed random environment

- Mathematics
- 2022

We consider random walks on the nonnegative integers in a space-time dependent random environment. We assume that transition probabilities are given by independent Beta(μ, μ) distributed random…

Half-space stationary Kardar–Parisi–Zhang equation beyond the Brownian case

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We study the Kardar–Parisi–Zhang (KPZ) equation on the half-line x ⩾ 0 with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recent work: they depend on…

An identity in distribution between full-space and half-space log-gamma polymers

- Materials Science
- 2021

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, (2) the point-to-line…

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