Hariharan Narayanan
Randomized Interior Point methods for Sampling and Optimization.
Mon, 11/23/2009 - 16:01 — SomNambulAuthors: Hariharan Narayanan
Subjects: Data Structures and Algorithms
AbstractAll known Markov Chains for sampling a general convex set have mixing times
that depend upon the aspect ratio of the convex set, a measure of which is the
ratio between the radius of the smallest sphere circumscribed around $K$ and
the radius of the largest sphere inscribed in $K$. Extending earlier work on
polytopes, we present a Markov chain for sampling from a convex body using a
self-concordant barrier, whose mixing time does not depend on its aspect ratio
or diameter.A Geometric Interpretation of Half-Plane Capacity.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Steven Lalley, Gregory Lawler, Hariharan Narayanan
Subjects: Probability
AbstractLet $A$ be a bounded, relatively closed subset of the upper half plane
$\mathbb{H}$ whose complement in $\mathbb{H}$ is simply connected. If $B_t$ is
a standard complex Brownian motion and $\tau_A = \inf\{t \geq 0: B_t \not \in
\mathbb{H} \setminus A\}$, the half-plane capacity of A, \[ \mathrm{cap}(A) :=
\lim_{y \to \infty}y \E^{iy}
User login
