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--- meetings_fall_2026 [2026/09/10 20:34] – avornor
+++ meetings_fall_2026 [2026/10/17 01:51] (current) – asjensen
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 | September 2  | Vertex-Minimal Subgraphs with K_n Minors | David Hathaway | Kansas State University | [[#september_2|Abstract]] |
 | September 9 | Computing Generalized Nash Equilibria with Quasi-Linear Constraints| Jiyoung Choi | Kansas State University |[[#september_9|Abstract]] |
-| September 16 | Notes on the Transfer-Impedance matrix.| Pietro Poggi-Corradini | Kansas State University |[[#september_16|Abstract]] |
+| September 16 | The Scaling Limit of Fair Peano Paths| Pietro Poggi-Corradini | Kansas State University |[[#september_16|Abstract]] |
-| September 23  | TBA | Pietro Poggi-Corradini | Kansas State University |  |
+| September 23  | The Scaling Limit of Fair Peano Paths | Pietro Poggi-Corradini | Kansas State University | [[#september_16|Abstract]] |
 | September 30  | Duality for the Dirichlet and Thomson problems on networks | Andrew Jensen | Kansas State University |  |
-| October 7  |  |  |  |  |
+| October 7  | **No Meeting** |  |  |  |
-| October 14  |  |  |  |  |
+| October 14  | **No Meeting** |  |  |  |
-| October 21  |  |  |  |  |
+| October 21  |  | Joan Lind | University of Tennessee, Knoxville |  |
 | October 28  |  |  |  |  |
 | November 4  |  |  |  |  |
 | November 11  |  |  |  |  |
 | November 18  |  |  |  |  |
-| November 25  | **No Meeting (fall break)** |  |  |  |
+| November 25  | **No Meeting** |  |  |  |
-| December 2  |  |  |  |  |
+| December 2  |  | Manisha Garg | University of Illinois, Urbana-Champaign |  |
-| December 9  |  |  |  |  |
+| December 9  |  | Sylvester Eriksson-Bique | University of Jyväskylä |  |
 ===== Abstracts =====
@@ Line 35: / Line 35: @@
 ==== September 16  ====
-This summer I started collecting some notes on this fascinating topic. I will start from the beginning and lay down the basic definitions, which means that I won't get to the Burton-Pemantle Theorem in one hour. However, that is the goal and hopefully we will get there in subsequent talks. After that we can start looking at the many applications of this matrix.
+ We study random Peano paths on planar square grids that arise from fair random spanning trees. These are trees that are sampled in such a way as to have the same (if possible) edge probabilities.
+In particular, we are interested in identifying the scaling limit as the mesh-size of the grid tends to zero.
+It is known that if the trees are sampled uniformly, then the scaling limit exists and equals ${\rm SLE}_8$. We show that if we simply follow the same steps as in
+[lawler-schramm-werner2002],
+then fair Peano paths have a deterministic scaling limit. We end by describing a different approach that is conjectured to have a non-deterministic scaling.