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** “ Self-avoiding walks “**

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Wednesday, 07. May. 2014 |
Audio-only-Recording as MP3-File
(smallest possible size):
- Audio.mp3 (ca.31Mb) ============================================ Video-Recording for any system with MP4-support:
- Video.mp4 (ca.274Mb) |
15:15 – 16:25 |

Abstract :

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, fueled 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.

Link:

http://www.math-stockholm.se/en/kalender/mireille-bousquet-melou-self-avoiding-walks-1.475111?date=2014-05-07&orgdate=2014-05-01&length=1&orglength=31

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