COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Squarings of rectangles

## Squarings of rectanglesAdd to your list(s) Download to your calendar using vCal - Addario-Berry, L (McGill University)
- Friday 24 April 2015, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Random Geometry Co-author: Nicholas Leavitt (McGill University) Growing random trees, maps, and squarings. We use a growth procedure for binary trees due to Luczak and Winkler, a bijection between binary trees and irreducible quadrangulations of the hexagon due to Fusy, Poulalhon and Schaeffer, and the classical angular mapping between quadrangulations and maps, to define a growth procedure for maps. The growth procedure is local, in that every map is obtained from its predecessor by an operation that only modifies vertices lying on a common face with some fixed vertex. The sequence of maps has an almost sure limit G; we show that G is the distributional local limit of large, uniformly random 3-connected graphs. A classical result of Brooks, Smith, Stone and Tutte associates squarings of rectangles to edge-rooted planar graphs. Our map growth procedure induces a growing sequence of squarings, which we show has an almost sure limit: an infinite squaring of a finite rectangle, which almost surely has a unique point of accumulation. We know almost nothing about the limit, but it should be in some way related to Liouville quantum gravity. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
## Other listsMEMS seminar RCEAL Tuesday Colloquia Psychology talks and events my_list Visual Rhetoric and modern South Asian history (2015-16) Fen Edge Archaeology Group## Other talksEquations in groups Primary liver tumor organoids: a new pre-clinical model for drug sensitivity analysis Tunable Functional Magnetic Skyrmions at Room Temperature Phylogenetic hypothesis of the Oleeae tribe (Oleaceae) Diversification and molecular evolution patterns in plastid and nuclear ribosomal DNA Animal Migration CGHR Practitioner Series: Sharath Srinivasan, Africa's Voices |