Mixed Moments for the Product of Ginibre Matrices

• URL: http://arxiv.org/abs/2007.10181v1
• Date: Mon, 20 Jul 2020 15:13:18 GMT
• Title: Mixed Moments for the Product of Ginibre Matrices
• Authors: Nick Halmagyi and Shailesh Lal
• Abstract summary: We find this ensemble is Gaussian with a variance matrix which is averaged over a multi-Wishart ensemble. We compute the mixed moments and find that at large $N$, they are given by an enumeration of non-crossing pairings weighted by Fuss-Catalan numbers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the ensemble of a product of n complex Gaussian i.i.d. matrices. We find this ensemble is Gaussian with a variance matrix which is averaged over a multi-Wishart ensemble. We compute the mixed moments and find that at large $N$, they are given by an enumeration of non-crossing pairings weighted by Fuss-Catalan numbers.

Related papers

• Discovering Sparse Representations of Lie Groups with Machine Learning [55.41644538483948]
  We show that our method reproduces the canonical representations of the generators of the Lorentz group. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.
  arXiv  Detail & Related papers  (2023-02-10T17:12:05Z)
• A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation [7.343886246061388]
  We propose an iterative matching algorithm, which succeeds in time as long as the correlation between the two Gaussian matrices does not vanish. Our result is the first algorithm that solves the graph matching type of problem when the correlation is an arbitrarily small constant.
  arXiv  Detail & Related papers  (2022-12-28T03:30:47Z)
• Non-PSD Matrix Sketching with Applications to Regression and Optimization [56.730993511802865]
  We present dimensionality reduction methods for non-PSD and square-roots" matrices. We show how these techniques can be used for multiple downstream tasks.
  arXiv  Detail & Related papers  (2021-06-16T04:07:48Z)
• A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups [115.58550697886987]
  We provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before. Our approach outperforms non-equivariant baselines, with applications to particle physics and dynamical systems.
  arXiv  Detail & Related papers  (2021-04-19T17:21:54Z)
• Quantum interpolating ensemble: Biorthogonal polynomials and average entropies [3.8265321702445267]
  The average of quantum purity and von Neumann entropy for an ensemble interpolates between the Hilbert-Schmidt and Bures-Hall ensembles. The proposed interpolating ensemble is a specialization of the $theta$-deformed Cauchy-Laguerre two-matrix model.
  arXiv  Detail & Related papers  (2021-03-07T01:56:08Z)
• Robustly Learning Mixtures of $k$ Arbitrary Gaussians [47.40835932474677]
  We give a-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $mathbbRd$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. Our main tools are an efficient emphpartial clustering algorithm that relies on the sum-of-squares method, and a novel tensor decomposition algorithm that allows errors in both Frobenius norm and low-rank terms.
  arXiv  Detail & Related papers  (2020-12-03T17:54:03Z)
• Robustly Learning any Clusterable Mixture of Gaussians [55.41573600814391]
  We study the efficient learnability of high-dimensional Gaussian mixtures in the adversarial-robust setting. We provide an algorithm that learns the components of an $epsilon$-corrupted $k$-mixture within information theoretically near-optimal error proofs of $tildeO(epsilon)$. Our main technical contribution is a new robust identifiability proof clusters from a Gaussian mixture, which can be captured by the constant-degree Sum of Squares proof system.
  arXiv  Detail & Related papers  (2020-05-13T16:44:12Z)
• On the covariance matrix for Gaussian states [0.0]
  We discuss how the criteria to characterize squeezing and entanglement using the covariance matrix give rise to new criteria in the symplectic matrix elements used to construct the general Gaussian states.
  arXiv  Detail & Related papers  (2020-03-24T18:39:48Z)
• Results on the algebraic matroid of the determinantal variety [16.54912614895861]
  We present a family of base sets of the matroid and conjecture these are all the base sets. This conjecture is reduced to a purely statement, which is proved for special cases.
  arXiv  Detail & Related papers  (2020-02-12T16:35:56Z)
• Optimal Iterative Sketching with the Subsampled Randomized Hadamard Transform [64.90148466525754]
  We study the performance of iterative sketching for least-squares problems. We show that the convergence rate for Haar and randomized Hadamard matrices are identical, andally improve upon random projections. These techniques may be applied to other algorithms that employ randomized dimension reduction.
  arXiv  Detail & Related papers  (2020-02-03T16:17:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.