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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Causal trees and Wigner&\;#39\;s semicircle law
- Ian McKeague (Columbia University)
DTSTART;TZID=Europe/London:20180424T110000
DTEND;TZID=Europe/London:20180424T120000
UID:TALK104302AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/104302
DESCRIPTION:Various aspects of standard model particle physics
might be explained by a suitably rich algebra act
ing on itself\, as suggested recently by Furey (20
15). This talk discusses the statistical behavior
of large causal tree diagrams that combine freely
independent elements in such an algebra. It is sho
wn that some of the familiar limiting distribution
s in random matrix theory (namely the Marchenko-Pa
stur law and Wigner'\;s semicircle law) emerge
in this setting as limits of normalized sums-over-
paths of non-negative elements of the algebra assi
gned to the edges of the tree. These results are e
stablished in the setting of non-commutative proba
bility. Trees with classically independent positiv
e edge weights (random multiplicative cascades) we
re originally proposed by Mandelbrot as a model di
splaying the fractal features of turbulence. The n
ovelty of the present approach is the use of non-c
ommutative (free) probability to allow the edge we
ights to take values in an algebra. Potential appl
ications in theoretical neuroscience related to Al
an Turing'\;s famous "Imitation Game" paper are
also discussed.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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