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SUMMARY:Mod-Phi Convergence: precise asymptotics and local limit theorems 
 for dependent random variables: III - Nikeghbali\, A (Universitt Zrich)
DTSTART:20141029T110000Z
DTEND:20141029T123000Z
UID:TALK55783@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We introduce a functional type of convergence from which one c
 an deduce central limit theorem type results\, as well as local limit theo
 rems and precise large and moderate deviations estimates. In particular th
 is provides us with a tool which predicts the scale up to which Gaussian a
 pproximation is valid and which explains quantitatively how a breaking of 
 symmetry occurs at this scale. On our way\, we also prove Berry-Esseen typ
 e estimates. We shall illustrate the methods with various examples:\n\n#su
 ms of dependent random variables with applications to the subgraph counts 
 in the Erdos-Renyi random graph model\;\n\n#examples from random combinato
 rial structures\;\n\n#examples from number theory\;\n\n#examples from rand
 om matrix theory.\n\n#examples from simple statistical mechanics models.\n
 \nAll these examples exhibit some dependence structure. Finally\, we shall
  try to see how these ideas can apply to some simple financial\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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