DSSYK, open ASEP/TASEP and 2d dilaton gravity at strong coupling
We discuss the triality between stochastic growth models in the KPZ universality class, the DSSYK model, and low dimensional dilaton gravity. The TASEP model, which will be our primary focus, is identified with the strong-coupling limit of two-dimensional quantum gravity. The Hamiltonian of DSSYK and the transfer matrix of ASEP coincide up to an additive constant, and we derive the exact expression for the resolvent of the corresponding transfer matrix in ASEP on a finite interval. We also mention the relation of cumulants with the Tutte polynomial $T(1,q)$ of the crossing graph dual to the chord diagram, which implies the relationship of the models considered with the $Q=0$ Potts model coupled with gravity. We further exploit the realization of all these models in terms of different versions of discrete and continuous random walks on two-dimensional manifolds, which parameterize the Hilbert spaces of the respective theories. The representation of TASEP as the growth model of heaps provides new insight into strong-coupling gravity, suggesting its interpretation as an emerging phenomenon. The new dualities between ASEP and q-TASEP models and heap models providing a useful growth interpretation have been developed.