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Probability Reading Group, Spring 2012 |
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| Covered Kasteleyn matrix, coupling function (a Cauchy kernel), convergence of the coupling function to $F_0, F_1$, which transform analytically under conformal maps. |
| 2/17 |
Dominos and the Gaussian Free Field |
Joe Chen |
| Clarified the connection between the coupling function and the Green's function, and showed how $F_0, F_1$ enter into the moment formula of the height variation. We didn't have time to prove convergence to GFF, but all the necessary technical lemmas have been covered, so please read on your own. |
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| 2/24 |
Discrete complex analysis |
Baris Ugurcan |
| See Mercat; Kenyon; Chelkak-Smirnov. |
| 3/1 (Th) |
Topics in potential theory |
Tianyi Zheng |
| 3/2 (Fr) is prospie visit day, so the meeting is tentatively moved to Th, time TBA. |
| 3/9 |
Hausdorff dimension of planar Brownian motion? |
Mark Cerenzia? |
| See Lawler-Schramm-Werner. |
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| 2/24 |
Discrete complex analysis on isoradial graphs |
Baris Ugurcan |
| Covered notions of harmonicity and holomorphicity on isoradial graphs, and showed how a sequence of uniformly bounded discrete harmonic functions on finer isoradial graph approximations converge in subsequence to a harmonic function in the continuum. |
| 3/2 |
No meeting |
| Prospie visit day |
| 3/9 |
Topics in potential theory |
Tianyi Zheng |
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| 3/16 |
No meeting |
| Day before spring break |
| 3/23 |
No meeting |
| Actual spring break |
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| 3/30 |
Meeting resumes? |
| Though Joe will be away at MSRI attending the Statistical Mechanics & Conformal Invariance workshop, he promises to bring home plenty of foods for thought. |
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| 3/30 |
Hausdorff dimension of planar Brownian motion |
Mark Cerenzia |
| See Lawler-Schramm-Werner. Some stochastic calculus will be covered. |
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Tentative syllabus (which is soon becoming outdated) |
