2026/03/31 by Anonymous, Sen Mu, Abbas Ali Saberi +2
Chemistry · Materials Science · Biochemistry, Genetics and Molecular Biology · #cond-mat.soft #cond-mat.dis-nn #math-ph #math.MP #physics.data-an
paper · pdf · doi:10.1103/cf3y-67f4
We numerically revisit the transfer-matrix formulation of directed polymers in random media and show that a common finite-dimensional framework organizes the canonical one-point fluctuation laws in (1+1) dimensions. For a fixed realization of the bulk disorder, full-space partition functions are obtained from the same time-ordered product W(t) through endpoint contractions or a Brownian-weighted initial vector, while the half-space construction modifies only the transfer rule at the absorbing boundary. These choices yield distributions consistent with the standard KPZ subclasses: Tracy--Widom GUE for point-to-point geometry, Tracy--Widom GOE for point-to-line geometry, Tracy--Widom GSE for half-space point-to-point geometry, and Baik--Rains for the stationary line-to-point construction. In all four cases, the free-energy fluctuations grow as t1/3, and the low-order cumulants approach the corresponding universal benchmarks. The matrix-product formulation also provides access to intrinsic spectral observables. For the leading eigenvalue λ1(t), the fluctuations of lnλ1(t) exhibit an intermediate t1/3 regime, while the standardized distribution remains distinct from the canonical benchmark laws over the studied time range.