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SUMMARY:Anticoncentration in Ramsey graphs and a proof of the Erdos-McKay 
 conjecture  - Mehtaab Sawhney (MIT) 
DTSTART:20221013T133000Z
DTEND:20221013T143000Z
UID:TALK183929@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION: An $n$-vertex graph is called $C$-Ramsey if it has no clique 
 or independent set of size $C\\log_2 n$ (i.e.\, if it has near-optimal Ram
 sey behavior). In this paper\, we study edge-statistics in Ramsey graphs\,
  in particular obtaining very precise control of the distribution of the n
 umber of edges in a random vertex subset of a $C$-Ramsey graph. This bring
 s together two ongoing lines of research: the study of ``random-like'' pro
 perties of Ramsey graphs and the study of small-ball probability for low-d
 egree polynomials of independent random variables.\n\nThe proof proceeds v
 ia an ``additive structure'' dichotomy on the degree sequence\, and involv
 es a wide range of different tools from Fourier analysis\, random matrix t
 heory\, the theory of Boolean functions\, probabilistic combinatorics\, an
 d low-rank approximation. One of the consequences of our result is the res
 olution of an old conjecture of Erdos and McKay\, for which he offered one
  of his notorious monetary prizes.\n\n(Joint work with Matthew Kwan\, Ashw
 in Sah and Lisa Sauermann)\n
LOCATION:MR12
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