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SUMMARY:A central limit theorem in the framework of the Thompson group F -
  Arundhathi Krishnan (Mary Immaculate College)
DTSTART:20241204T115000Z
DTEND:20241204T123000Z
UID:TALK218632@talks.cam.ac.uk
DESCRIPTION:The classical central limit theorem&nbsp\;states that the aver
 age of an infinite&nbsp\;sequence of independent and identically distribut
 ed random variables\, when suitably rescaled\, tends to a normal distribut
 ion. In fact\, this classical result can be stated purely algebraically\, 
 using the combinatorics of pair partitions.&nbsp\; In the 1980s\, Voicules
 cu proved an analog of the central limit theorem in free probability theor
 y\,&nbsp\;&nbsp\;wherein the normal distribution is replaced by Wigner's s
 emicircle distribution.&nbsp\;Later\, Speicher provided an algebraic&nbsp\
 ;proof of the free central limit theorem\, based on the combinatorics of n
 on-crossing pair partitions. Since then\, various algebraic central limit 
 theorems have been studied in&nbsp\;noncommutative probability\, for insta
 nce\, in the context of symmetric groups. My talk will discuss a central l
 imit theorem for the Thompson group F\, and show that the central limit la
 w of a naturally defined sequence in the group algebra of F is the normal 
 distribution. Our combinatorial approach employs abstract reduction system
 s to arrive at this result.&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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