Theoretical Statistics and Mathematics Unit, ISI Delhi

April 1, 2015 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Kumarjit Saha,
Indian Statistical Institute, Delhi

Title:
Directed spanning forest

Abstract of Talk

The directed spanning forest(DSF) was introduced by Baccelli and
Bordenave. Consider a homogeneous Poisson point process ${\cal N}$ on
$\mathbb{R}^d$. The DSF on $\mathbb{R}^d$ with direction $e_d$ is the
random graph with vertex set ${\cal N}$ and edge set $E = \{__: u
\in {\cal N}\}$ where $h(u)$ is the nearest point in ${\cal N}$ to $u$
having strictly larger $d$ th co-ordinate. Coupier and Tran showed that
for $d=2$, DSF consists of a single tree almost surely. We show that
for $d=2,3$, DSF consists of a single tree nad for $d\geq 4$, DSF is a
forest with infinitely many disjoint trees almost surely. This is a joint
work with David Coupier, Anish Sarkar and Viet Chi Tran.
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