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The one-dimensional KPZ equation and the Airy process

- S. Prolhac, H. Spohn
- Mathematics
- 24 January 2011

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a… Expand

Two-point generating function of the free energy for a directed polymer in a random medium

- S. Prolhac, H. Spohn
- Physics
- 17 November 2010

We consider a (1 + 1)-dimensional directed continuum polymer in a Gaussian delta-correlated spacetime random potential. For this model the moments (= replica) of the partition function, Z(x, t), can… Expand

The matrix product solution of the multispecies partially asymmetric exclusion process

- S. Prolhac, M. Evans, K. Mallick
- Mathematics
- 17 December 2008

We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product… Expand

Finite-Time Fluctuations for the Totally Asymmetric Exclusion Process.

- S. Prolhac
- Mathematics, PhysicsPhysical review letters
- 12 November 2015

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Tree structures for the current fluctuations in the exclusion process

- S. Prolhac
- Physics
- 18 November 2009

We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the… Expand

Cumulants of the current in a weakly asymmetric exclusion process

- S. Prolhac, K. Mallick
- Mathematics
- 3 February 2009

We study the fluctuations of the total current for a partially asymmetric exclusion process in the scaling of a weak asymmetry (asymmetry of order the inverse of the size of the system) using the… Expand

The propagator of the attractive delta-Bose gas in one dimension

- S. Prolhac, H. Spohn
- Mathematics, Physics
- 15 September 2011

We consider the quantum δ-Bose gas on the infinite line. For repulsive interactions, Tracy and Widom have obtained an exact formula for the quantum propagator. In our contribution we explicitly… Expand

Large deviations of surface height in the 1 + 1-dimensional Kardar–Parisi–Zhang equation: exact long-time results for λH<0

- P. Sasorov, B. Meerson, S. Prolhac
- Mathematics, Physics
- 9 March 2017

We study atypically large fluctuations of height H in the 1 + 1-dimensional Kardar–Parisi–Zhang (KPZ) equation at long times t, when starting from a ‘droplet’ initial condition. We derive exact… Expand

Current fluctuations in the exclusion process and Bethe ansatz

- S. Prolhac, K. Mallick
- Mathematics
- 30 January 2008

We use the Bethe ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled… Expand

Fluctuations and skewness of the current in the partially asymmetric exclusion process

- S. Prolhac
- Mathematics
- 27 May 2008

We use functional Bethe ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulae for the first two cumulants (mean… Expand

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