All reports by Author Penghui Yao:

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TR21-178
| 3rd December 2021
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Srinivasan Arunachalam, Oded Regev, Penghui Yao#### On the Gaussian surface area of spectrahedra

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TR21-013
| 20th January 2021
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Srinivasan Arunachalam, Penghui Yao#### Positive spectrahedrons: Geometric properties, Invariance principles and Pseudorandom generators

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TR17-010
| 18th January 2017
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Xiaodi Wu, Penghui Yao, Henry Yuen#### Raz-McKenzie simulation with the inner product gadget

Revisions: 1

Srinivasan Arunachalam, Oded Regev, Penghui Yao

We show that for sufficiently large $n\geq 1$ and $d=C n^{3/4}$ for some universal constant $C>0$, a random spectrahedron with matrices drawn from Gaussian orthogonal ensemble has Gaussian surface area $\Theta(n^{1/8})$ with high probability.

more >>>Srinivasan Arunachalam, Penghui Yao

In a recent work, O'Donnell, Servedio and Tan (STOC 2019) gave explicit pseudorandom generators (PRGs) for arbitrary $m$-facet polytopes in $n$ variables with seed length poly-logarithmic in $m,n$, concluding a sequence of works in the last decade, that was started by Diakonikolas, Gopalan, Jaiswal, Servedio, Viola (SICOMP 2010) and Meka, ... more >>>

Xiaodi Wu, Penghui Yao, Henry Yuen

In this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions $f$ composed with the Inner Product gadget $g_{IP}(x,y) = \sum_i x_iy_i \mathrm{mod} \, 2$ of logarithmic size. In other words, given a function $f: ... more >>>