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SUMMARY:Moumanti Podder (NYU Shanghai)
DTSTART:20201116T140000Z
DTEND:20201116T150000Z
DTSTAMP:20260423T052457Z
UID:EPC/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/27/">Som
 e combinatorial games on rooted multi-type Galton-Watson trees</a>\nby Mou
 manti Podder (NYU Shanghai) as part of Extremal and probabilistic combinat
 orics webinar\n\n\nAbstract\nIn a rooted multi-type Galton-Watson branchin
 g process\, the root is assigned a colour from a finite set $\\Sigma$ of c
 olours according to some probability distribution P\, and a vertex of the 
 tree\, conditioned on its colour $\\sigma \\in \\Sigma$\, gives birth to o
 ffspring according to some probability distribution $\\chi_{\\sigma}$ on $
 \\mathbb{N}_{0}^{\\Sigma}$. In particular\, one may consider $\\Sigma = \\
 {{\\rm red}\, {\\rm blue}\\}$ and the resulting random tree\, denoted T\, 
 can be viewed as a directed random graph if each edge is attributed a dire
 ction from parent to child. I consider the normal\, misere and escape game
 s on T\, each played between P1 and P2\, with P1 being allowed to move the
  token only along monochromatic directed edges and P2 being allowed to mov
 e the token only along non-monochromatic directed edges. I then investigat
 e the probabilities of win\, loss and (where pertinent) draw of each playe
 r as fixed points of distributional recursions\, establish inequalities be
 tween win / loss / draw probabilities of the players across different game
 s\, seek possible phase transitions in win / loss / draw probabilities as 
 the parameters involved in the offspring distributions are made to vary\, 
 study expected durations of the games etc.\n
LOCATION:https://researchseminars.org/talk/EPC/27/
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