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math.PR2022★ 1 cited
The Green's function of the parabolic Anderson model and the continuum directed polymer
Tom Alberts, Christopher Janjigian, Firas Rassoul-Agha +1
We build a regular version of the field which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing…
math.PR2022★ 13 cited
The stationary horizon and semi-infinite geodesics in the directed landscape
Ofer Busani, Timo Seppäläinen, Evan Sorensen
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive sc…