Mireille Bousquet-Mélou: Self-avoiding walks

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Time: Wed 2014-05-07 14.15 - 16.15

Lecturer: Mireille Bousquet-Mélou, CNRS and Université de Bordeaux 1

Schedule

14:15-15:00: Precolloquium for PhD and master students by Erik Aas, KTH (Room FB42, Albanova)

15:15-16:15: Colloquium lecture by by Mireille Bousquet-Mélou (Room Oskar Klein, Albanova)

16:15-17:00: SMC social get together with refreshments

Abstract (Colloquium)

A lattice walk is said to be self-avoiding if it never visits the same vertex twice. These simple objects were introduced in physics in the
1940's as a natural model of polymers. Since then, their study, fuelled by beautiful predictions often coming from statistical
physics, has become an important question in combinatorics and probability theory.


As for many lattice models, the properties of self-avoiding walks (SAWs) are better understood in high dimension. Roughly speaking, in dimension 5 and beyond, the properties of SAWs resemble those of random walks (Hara-Slade, 1992). I will focus on the tricky dimension 2, where the most elementary questions remain unsolved: what is, asymptotically, the number of n-step SAWs? What is, on average, their end-to-end distance? Simple answers to these questions have been conjectured decades ago, yet they have resisted all proving attempts so far.

I will describe some classical tools, like unfolding and pivot moves. I will also cover a recent major progress due to Duminil-Copin and Smirnov, which deals with SAW on the hexagonal lattice, and some variations on this result.

Kollokvier 2014

Titel Datum
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Irene Fonseca: Variational Methods in Materials and Image Processing 1409736300388 2014‑09‑03
Ib Madsen: Moduli Spaces and Topology 1402468380014 2014‑06‑11
Mikko Salo: Can one hear the shape of a space? 1395882406905 2014‑03‑27
Svante Janson: Random Graphs 1391000400879 2014‑01‑29
Mireille Bousquet-Mélou: Self-avoiding walks 1399467600358 2014‑05‑07
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