clopen.solutions

Open problems

980 registered problems.

OP-00030 Open
Sub-exponential detection in the hard regime of multi-frequency synchronization
ST · group synchronization · Randomstrasse101 · spiked random matrices · statistical-to-computational gaps
OP-00054 Solution claimed
The spectral threshold of Kikuchi matrices for tensor PCA
PR · Kikuchi hierarchy · random matrices · Randomstrasse101 · statistical-to-computational gaps · tensor PCA
OP-00059 Solution claimed
Sharp norm bounds for graph matrices
PR · graph matrices · matrix chaos · random matrices · Randomstrasse101 · Sum-of-Squares
OP-00060 Solution claimed
The value of ω(A) for Gaussian matrices in real phase retrieval
PR · phase retrieval · random matrices · Randomstrasse101 · stability
OP-00061 Solution claimed
The Matrix Spencer conjecture
CO · discrepancy theory · Matrix Spencer · random matrices · Randomstrasse101
OP-00063 Solution claimed
A diverging number of frequencies in multi-frequency synchronization
ST · group synchronization · Randomstrasse101 · spiked random matrices · statistical-to-computational gaps
OP-00065 Open
A critical number of frequencies for weak recovery in multi-frequency synchronization
ST · group synchronization · low-degree polynomials · spiked random matrices · statistical-to-computational gaps
OP-00173 Open
Super-exponential decay of the zero-permanent probability
PR · anticoncentration · OpenProblemsInNLA · permanents · random matrices
OP-00209 Solution claimed
Sharp sparsity threshold for injectivity of a random sparse rectangular matrix
PR · OpenProblemsInNLA · smallest singular values · sparse random matrices · subspace injections
OP-00218 Solution claimed
The square-root upper bound for Gaussian partial-pivoting growth
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · random matrices
OP-00225 Solution claimed
Sharp row-deletion singular-value limit for spherical random matrices
NA · Kaczmarz methods · OpenProblemsInNLA · random matrices · smallest singular values
OP-00229 Solution claimed
Spectral-gap-independent constants for randomized block polynomial interpolation
NA · block Lanczos methods · matrix polynomials · OpenProblemsInNLA · random matrices
OP-00251 Solution claimed
Sharp parameter dependence for structured Gaussian operator norms
PR · OpenProblemsInNLA · operator norms · random matrices
OP-00274 Solution claimed
Sharp least-singular-value bounds for independent random tensor columns
PR · AIM Open Applied Problems · random matrices · random tensors · singular values
OP-00472 Open
GOE level spacings in a desymmetrized Sinai billiard
SP · AIM Open Applied Problems · level spacings · quantum chaos · random matrices