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Statistical thresholds for Tensor PCA
We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximumExpand
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Universality of the least singular value for sparse random matrices
We study the distribution of the least singular values associated to an ensemble of sparse random matrices. Our motivating example is the ensemble of $N\times N$ matrices whose entries are chosenExpand
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Schatten-class Truncated Toeplitz Operators
We investigate truncated Toeplitz operators belonging to the Schatten ideals. We completely characterize such operators when they have an analytic symbol or belong to the ideal of Hilbert-SchmidtExpand
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An Improved Lower Bound for Sparse Reconstruction from Subsampled Hadamard Matrices
TLDR
We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. Expand
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Tail bounds for gaps between eigenvalues of sparse random matrices
We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and error probabilityExpand
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Sparse Reconstruction from Hadamard Matrices: A Lower Bound
TLDR
We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. Expand
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GOE Statistics for Levy Matrices
In this paper we establish eigenvector delocalization and bulk universality for L\'{e}vy matrices, which are real, symmetric, $N \times N$ random matrices $\textbf{H}$ whose upper triangular entriesExpand
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Formulas for odd zeta values and powers of .
Plouffe conjectured fast converging series formulas for π and ζ(2n+1) for small values of n. We find the general pattern for all integer values of n and offer a proof.
The Connectivity of Wavelets
TLDR
is published by the Office of Undergraduate Research once a semester each academic year. Expand
ARTU Report Fall 2014: Truncated Toeplitz Operators
I spent this summer doing research on truncated Toeplitz operators under the supervision of Professor Rochberg. Classical Toeplitz operators are defined on the Hardy space H2(T). If f ∈ L∞(T) and MfExpand
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