Intermediate Disorder regime for half-space directed polymers

Abstract

We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel in [AKQ]. By scaling the inverse temperature like $\beta n^{-1/4}$, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. We also apply our convergence results to the exact-solvable log-gamma directed polymer model in a half-space.

27 pages

References in corpus (2)

• The KPZ Limit of ASEP with Boundary
• Singular SPDEs in domains with boundaries

Cited by in corpus (3)

• Half-space Macdonald processes
• The lower tail of the half-space KPZ equation
• Lyapunov exponents of the half-line SHE