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math.PR2022★ 2 cited
Discrete geodesic local time converges under KPZ scaling
Shirshendu Ganguly, Lingfu Zhang
The directed landscape constructed in (Dauvergne-Ortmann-Virag '18) produces a directed, planar, random geometry, and is believed to be the universal scaling limit of two-dimension…
math.PR2022★ 6 cited
Cutoff profile of the Metropolis biased card shuffling
Lingfu Zhang
We consider the Metropolis biased card shuffling (also called the multi-species ASEP on a finite interval or the random Metropolis scan). Its convergence to stationary was believed…
math.PR2022★ 5 cited
Fractal geometry of the space-time difference profile in the directed landscape via construction of geodesic local times
Shirshendu Ganguly, Lingfu Zhang
The Directed Landscape, a random directed metric on the plane (where the first and the second coordinates are termed spatial and temporal respectively), was constructed in the brea…