BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:5117@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240409T143000
DTEND;TZID=Europe/Paris:20240409T153000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/genealogies-of-records-of-stoch
 astic-processes-with-stationary-increments-as-unimodular-trees/
SUMMARY: (...): Genealogies of records of stochastic processes with station
 ary increments as unimodular trees.
DESCRIPTION:: Abstract:  Consider a stationary sequence $X=(X_n)$ of integ
 er-valued random variables with mean $m in [-infty\, infty]$. Let $S=(S_n)
 $ be the stochastic process with increments $X$ and such that $S_0=0$. For
  each time $i$\, draw an edge from $(i\,S_i)$ to $(j\,S_j)$\, where $j&gt\
 ;i$ is the smallest integer such that $S_j geq S_i$\, if such a $j$ exists
 . This defines the record graph of $X$.\n\nWe show that if $X$ is ergodic\
 , then its record graph exhibits the following phase transitions when $m$ 
 ranges from  $-infty$ to $infty$. For $m&lt\;0$\, the record graph has in
 finitely many connected components which are all finite trees. At $m=0$\, 
 it is either a one-ended tree or a two-ended tree. For $m&gt\;0$\, it is a
  two-ended tree.\n\n\nWe analyse the distribution of the component of $0$ 
 in the record graph when $X$ is an i.i.d. sequence of random variables who
 se common distribution is supported on ${-1\,0\,1\,ldots}$\, making $S$ a 
 skip-free to the left random walk. For this random walk\, if $m&lt\;0$\, t
 hen the component of $0$ is a unimodular typically re-rooted Galton-Watson
  Tree. If $m=0$\, then the record graph rooted at $0$ is a one-ended unimo
 dular random tree\, specifically\, it is a unimodular Eternal Galton-Watso
 n Tree. If $m&gt\;0$\, then the record graph rooted at $0$ is a unimodular
 ised bi-variate Eternal Kesten Tree.\n\n\nA unimodular random directed tre
 e is said to be record representable if it is the component of $0$ in the 
 record graph of some stationary sequence. We show that every infinite unim
 odular ordered directed tree with a unique succession line is record repre
 sentable. In particular\, every one-ended unimodular ordered directed tree
  has a unique succession line and is thus record representable.
CATEGORIES:Séminaire,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20240331T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR