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UID:www.tcs.tifr.res.in/event/1069
DTSTAMP:20230914T125949Z
SUMMARY:On Realizable Distributions
DESCRIPTION:Speaker: Siddharth Bhandari\n\nAbstract: \nJoin Zoom Meeting\nh
 ttps://zoom.us/j/98172222418?pwd=b0htSDQ5NDRKQ050K0d6cHJ3YnZXQT09\nMeeting
  ID: 981 7222 2418\nPassword: studsem\nAbstract: Coupling arguments are co
 mmonplace in approximate and perfect sampling. A coupling is a joint distr
 ibution between RVs: it helps us relate and compare distributions of the R
 Vs.\n\nWe will study the following:\nGiven RVs X_1\, X_2\, X_3\, X_4\,....
 \, X_n each taking a value in $\\Omega$ and marginally distributed accordi
 ng to $\\mu_1\, \\mu_2\, ...\, \\mu_n$ on $\\Omega^n$\, we say a RV $Y$ di
 stributed according to $\\tau$ is realizable wrt to $X_1\,...\, X_n$ iff f
 or all joint distributions $\\mu$ of $X_1\,..\, X_n$ such that each $X_i~\
 \mu_i$ there exists a joint distribution  $\\mu'$ of $X_1\,...\, X_n\, Y$
  such that 1> $(X_1\, X_2\, ...\, X_n)~\\mu$  and $Y~\\tau$ 2> Pr_{\\mu
 '}[Y\\in {X_1\,...\, X_n}]=1.\nWe will show that  a distribution $\\tau$ 
 is realizable wrt to $\\mu_1\,..\, \\mu_n$ iff for all $S\\subseteq \\Omeg
 a$ we have: $\\mu_i(S)\\leq \\tau(S)\\leq \\mu_j (S)$ for some $i\,j\\in [
 n]$.\n
URL:https://www.tcs.tifr.res.in/web/events/1069
DTSTART;TZID=Asia/Kolkata:20200711T160000
DTEND;TZID=Asia/Kolkata:20200711T170000
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