Hi all,
Tomorrow, Monday Sept 26 at 2:10-3:00pm in Fields Institute room 210, Evan Sorensen will give a seminar. Note that the seminar time has moved forward by one hour compared to the previous week.
Title: The stationary horizon and semi-infinite geodesics in the directed landscape.
Abstract: The stationary horizon (SH) is a stochastic process of coupled Brownian
motions indexed by their real-valued drifts. It was first introduced
Busani as the diffusive scaling limit of the Busemann process of
exponential last-passage percolation. It was independently discovered as
the Busemann process of Brownian last-passage percolation by
Seppalainen and Sorensen. We show that SH is the unique invariant
distribution and an attractor of the KPZ fixed point under conditions on
the asymptotic spatial slopes. It follows that SH describes the
Busemann process of the directed landscape. This gives control of
semi-infinite geodesics simultaneously across all initial points and
directions. The countable dense set Ξ of directions of discontinuity of
the Busemann process is the set of directions in which not all geodesics
coalesce and in which there exist at least two distinct geodesics from
each initial point. This creates two distinct families of coalescing
geodesics in each Ξ direction. In Ξ directions, the Busemann difference
profile is distributed as Brownian local time. We describe the point
process of directions ξ ∈ Ξ and spatial locations where the ξ ±
Busemann functions separate. Based on joint work with Ofer Busani and
Timo Seppalainen.