| Date | Speaker | content |
|---|---|---|
| 09/20/2023 | Jiyue Zeng | Introductions of Last Passage Time, Airy Line Ensembles, Airy process, melon map, Brownian Last Passage Percolations. |
| 09/27/2023 | Jiyue Zeng | We discuss section three of the paper which covers the basic geometric properties of last passage time and last passage path. |
| 10/11/2023 | Victor Hugo Daniel | We discuss section four of the paper which proves that the last passage percolation over a set of continuous functions is the same as the last passage percolation over the melon maps, i.e., f[(x,n) -> (y,1)] = Wf[(x,n) -> (y,1)]. |
| 10/18/2023 | Hindy Drillick | We discuss section five of the paper which covers the important result that last passage percolation across the bottom n-k lines can be translated to the backward first passage percolation over the top k lines. |
| 10/25/2023 | Jiyue Zeng | We discuss the first part of chapter six of the paper. We will discuss Airy Line Ensembles as the scaling limit of last passage percolations over Brownian melons and we characterize the mean and fluctuations of LPP in this form, WB[(x,n) -> (z,k)]. |
| 11/01/2023 | Jiyue Zeng | We discuss the second part of chapter six of the paper. We will use the theorems proved last time to characterize the mean and fluctuations of LPP over Airy Line Ensembles, i.e., A[(x,n) -> (z,k)]. |
| 11/08/2023 | Zoe Himwich | We discuss the first lemma from chapter 7. It shows the concentration of jump time from K+1st line to Kth line in last passage percolation over Brownian melon. |
| 11/15/2023 | Zoe Himwich | We discuss the second lemma from chapter 7. It shows that under the condition that initial starting locations are close enough, two brownian last passage paths will almost surely intersect. |
| 11/29/2023 | Victor Hugo Daniel | We discuss chapter 8. We will prove uniqueness in law and existence of Airy sheet. We start by proving tightness. |
| 12/06/2023 | Victor Hugo Daniel | We continue the discussion last time on constructing Airy sheet. |