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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240603T150000
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TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240603T160000
URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-182
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:Speaker: Manuel Fernandez\, Georgia Tech\n\n_\"On the $\\ell_0$
 -Isoperimetry of Measurable Sets\"_\n\nGibbs-sampling\, also known as coor
 dinate hit-and-run (CHAR)\, is a\nrandom walk used to sample points unifor
 mly from convex bodies. Its\ntransition rule is simple: Given the current 
 point p\, pick a random\ncoordinate i and resample the i'th coordinate of 
 p according to the\ndistribution induced by fixing all other coordinates. 
 Despite its use\nin practice\, strong theoretical guarantees regarding the
  mixing time\nof CHAR for sampling from convex bodies were only recently s
 hown in\nworks of Laddha and Vempala\, Narayanan and Srivastava\, and Nara
 yanam\,\nRajaraman and Srivastava. In the work of Laddha and Vempala\, as 
 part\nof their proof strategy\, the authors introduced the notion of the\n
 $\\ell_0$ isoperimetric coefficient of a measurable set and provided a\nlo
 wer bound for the quantity in the case of axis-aligned cubes. In\nthis tal
 k we will present some new results regarding the $\\ell_0$\nisoperimetric 
 coefficient of measurable sets. In particular we pin\ndown the exact order
  of magnitude of the $\\ell_0$ isoperimetric\ncoefficient of axis-aligned 
 cubes and present a general upper bound of\nthe $\\ell_0$ isoperimetric co
 efficient for any measurable set. As an\napplication\, we will mention how
  the results give a moderate\nimprovement in the mixing time of CHAR.\n\nM
 C 5501
DTSTAMP:20260512T220444Z
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