Please Note: This seminar will be given online.
|
Probability seminar series
Dan
Mikulincer Link to join seminar: Hosted on Webex |
A central limit theorem for tensor powers
We
introduce
the
Wishart
tensor
as
the
p-th
tensor
power
of
a
given
random
vector
X
in
R^n.
This
is
inspired
by
the
classical
Wishart
matrix,
obtained
when
p=2.
Sums
of
independent
Wishart
tensors
appear
naturally
when
studying
random
geometric
graphs
as
well
as
universality
phenomena
in
large
neural
networks
and
we
will
discuss
possible
connections
and
recent
results.
The
main
focus
of
the
talk
will
be
quantitative
estimates
for
the
central
limit
theorem
of
Wishart
tensors.
In
this
setting,
we
will
explain
how
Stein's
method
may
be
used
to
exploit
the
low
dimensional
structure
which
is
inherent
to
tensor
powers.
Specifically,
it
will
be
shown
that,
under
appropriate
regularity
assumptions,
a
sum
of
independent
Wishart
tensors
is
close
to
a
Gaussian
tensor
as
soon
as
n^(2p-1)<<d.
Here,
n
is
the
dimension
of
the
random
vector
and
d
is
the
number
of
independent
copies.