The cover time of a graph is one of the most basic and
well-studied properties of the simple random walk, and yet a number
of fundamental questions concerning cover times have remained open.
We show that there is a deep connection between cover...
Intensive study throughout the last three decades has yielded a
rigorous understanding of the spectral-gap of the Glauber dynamics
for the Ising model on Z2 everywhere except at criticality. While
the critical behavior of the Ising model has long...
We consider the problem of approximately solving a system of
homogeneous linear equations over reals, where each equation
contains at most three variables. Since the all-zero assignment
always satisfies all the equations exactly, we restrict the...
In this talk we will present a near-optimal compression scheme
for bounded-round randomized 2-party communication protocols.
Previously, such a scheme was only known for protocols where the
inputs to the parties are independent. The results yield a...
We give a simple combinatorial proof of the Chernoff-Hoeffding
concentration
bound for sums of independent Boolean random variables. Unlike the
standard
proofs, our proof does not rely on the method of higher moments,
but rather uses
an intuitive...
Semidefinite programming bounds are widely used in combinatorial
optimization, quantum computing and complexity theory. The first
semidefinite programming bound to gain fame is the so-called theta
number developed by Lov\'asz to compute the Shannon...
We shall discuss new pseudorandom generators for regular
read-once branching programs of small width. A branching program is
regular if the in-degree of every vertex in it is (either 0 or) 2.
For every width d and length n, the pseudorandom...
In this survey I will present several extremal problems, and
some solutions, concerning convex lattice polytopes.
A typical example is to determine the smallest area that a convex
lattice polygon can have if it has exactly n vertices.
Collateralized Default Obligations (CDOs) and related financial
derivatives have been at the center of the last financial crisis
and subject of ongoing regulatory overhaul.
Despite their demonstrable benefits in economic theory, derivatives
suffer...
