Tomohiro Sasamoto

From duality to determinants for q-TASEP and ASEP

We prove duality relations for two interacting particle systems: the

Spectral theory for the q-Boson particle system

q

Asymmetric Stochastic Transport Models with Uq(su(1,1)) Symmetry

-deformed totally asymmetric simple exclusion process (

Determinantal Structures in the O’Connell-Yor Directed Random Polymer Model

q

Large Deviations of a Tracer in the Symmetric Exclusion Process

-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents, respectively. Duality implies that they solve systems of ODEs. These systems are integrable and for particular step and half-stationary initial data we use a nested contour integral ansatz to provide explicit formulas for the systems solutions, and hence also the moments. We form Laplace transform-like generating functions of these moments and via residue calculus we compute two different types of Fredholm determinant formulas for such generating functions. For ASEP, the first type of formula is new and readily lends itself to asymptotic analysis (as necessary to reprove GUE Tracy--Widom distribution fluctuations for ASEP), while the second type of formula is recognizable as closely related to Tracy and Widoms ASEP formula [Comm. Math. Phys. 279 (2008) 815--844, J. Stat. Phys. 132 (2008) 291--300, Comm. Math. Phys. 290 (2009) 129--154, J. Stat. Phys. 140 (2010) 619--634]. For

Free energy distribution of the stationary O’Connell–Yor directed random polymer model

q

Point-interacting Brownian motions in the KPZ universality class

-TASEP, both formulas coincide with those computed via Borodin and Corwins Macdonald processes [Probab. Theory Related Fields (2014) 158 225--400]. Both

Combinatorics of the asymmetric exclusion process on a semi-infinite lattice

q

The 1D Kardar-Parisi-Zhang equation: Height distribution and universality

-TASEP and ASEP have limit transitions to the free energy of the continuum directed polymer, the logarithm of the solution of the stochastic heat equation or the Hopf--Cole solution to the Kardar--Parisi--Zhang equation. Thus,

Spectral Theory for Interacting Particle Systems Solvable by Coordinate Bethe Ansatz

q