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TZID:Asia/Jerusalem
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DTSTART:20171029T020000
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UID:calendar.49252.field_date.0@mathematics.huji.ac.il
DTSTAMP:20210126T221026Z
CREATED:20171228T140010Z
DESCRIPTION:Date: \n\n12:00pm to 1:00pm\n\n\n\n\nSee also: Dynamics Lunch
\, Events & Seminars\, Seminars\n\n\n\nAn M-dependent process X(n) on the
integers\, is a process for which every event concerning with X(-1)\,X(-2)
\,... is independent from every event concerning with X(M)\,X(M+1)\,... \n
Such processes play an important role both as scaling limits of physical s
ystems and as a tool in approximating other processes. \n A question tha
t has risen independently in several contexts is:\n'is there an M dependen
t proper colouring of the integer lattice for some finite M?'\n Ramsey t
heory guarantees that the most standard way of producing an M-dependent pr
ocess can never produce such a colouring. That is\, defining X(i)=f(Y(i)\,
Y(i+1)\,...\,Y(i+M)) where Y(n) are uniform([0\,1]) i.i.d. (such processes
are called M+1-block factors). It was therefore conjectured to be impossi
ble.\n After a short introduction to the history of the problem\, I w
ill describe a recent simple construction of Holryd and Liggett refuting t
his conjecture. Giving a 1-dependent proper 4-colouring and a 2-dependent
proper 3-colouring of the integer lattice\, which are produced in an entir
ely new manner via an insertion process.\n\n Export\n \n\n \nsubscribe
iCal
DTSTART;TZID=Asia/Jerusalem:20180102T120000
DTEND;TZID=Asia/Jerusalem:20180102T130000
LAST-MODIFIED:20191103T130312Z
SUMMARY:Dynamics Lunch: Ohad Feldheim (HUJI) 'Finitely dependent proper col
ouring of Z'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/dynamics-lunch-ohad-feldh
eim
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