Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > GAUSSIAN SPACE:
Reports tagged with Gaussian Space:
TR09-144 | 24th December 2009

#### An Invariance Principle for Polytopes

Let $X$ be randomly chosen from $\{-1,1\}^n$, and let $Y$ be randomly
chosen from the standard spherical Gaussian on $\R^n$. For any (possibly unbounded) polytope $P$
formed by the intersection of $k$ halfspaces, we prove that
\left|\Pr\left[X \in P\right] - \Pr\left[Y \in P\right]\right| \leq \log^{8/5}k ... more >>>

TR11-051 | 8th April 2011
Thomas Vidick

#### A concentration inequality for the overlap of a vector on a large set, With application to the communication complexity of the Gap-Hamming-Distance problem

Given two sets $A,B\subseteq\R^n$, a measure of their dependence, or correlation, is given by the expected squared inner product between random $x\in A$ and $y\in B$. We prove an inequality showing that no two sets of large enough Gaussian measure (at least $e^{-\delta n}$ for some constant $\delta >0$) ... more >>>

ISSN 1433-8092 | Imprint