Title: Asymptotic Distribution of Parameters in Random Maps
| Speaker: | Julien Courtiel |
| Affiliation: | Universite de Caen in France |
| Room: | MC 6486 |
Abstract:
A
rooted
map
is
a
connected
graph
in
which
the
half-edges
have
been
cyclically
ordered
around
each
vertex.
This
talk
addresses
the
question
of
the
asymptotic
behavior
of
several
parameters
of
maps
(such
as
number
of
vertices,
the
root
degree)
without
any
constraint
on
the
genus
of
the
maps.
Although
this
perspective
is
quite
opposed
to
the
classical
one
where
maps
model
discrete
surfaces
(and
so
where
the
genus
is
important),
this
has
numerous
applications
in
transverse
scientific
areas,
like
Quantum
Field
Theory
or
lambda-calculus.
Thus,
as
a
motivation,
we
begin
by
introducing
the
existing
connexions
between
combinatorial
maps
and
other
families
of
objects.
Then,
we
explain
the
(new!)
techniques
required
to
solve
the
underlying
enumerative
problem,
and
show
why
they
must
differ
from
the
ones
used
when
the
genus
is
fixed.
Finally,
we
stand
back
a
bit,
and
ask
ourselves
whether
the
asymptotic
results
could
have
been
thought
ahead,
given
the
previously
mentioned
combinatorial
connexions.
This
is
a
joint
work
with
Olivier
Bodini,
Sergey
Dovgal
and
Hsien-Kuei
Hwang.