In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value , when the number of rows of the matrices becomes very large. These results provide probabilistic description or picture on the behaviors of the largest p -singular values of random matrices in probability for p> 1.
In this paper, we study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the q-quasinorm with 0 < q ≤ 1. March 15, 2016 by Louis Y. Liu Leave a comment.
Email: [name]@stanford.edu Office: E2-341A.
satisfying are modified Dirac delta functions. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices. Math Colloquium Schedule; Number Theory/Arithmetic Geometry; SMARTS ; Topology ; Placement. Yang Liu, SISSA. The infinity norm is often used as a model in analysis and geometry, not for continuous scenarios, but for the discrete or singular scenarios. I am interested in theoretical computer science at large, especially algorithm design. Yang Liu is a philosopher at University of Cambridge.
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Yang Liu's interests include logic, decision theory, foundations of probability, philosophy of ai.
In this paper, the p -singular values of random matrices with Gaussian entries defined in terms of the l p -p -norm for p> 1, as is studied.
eliminates the feasibility of sifting out the maximal modulus. Currently, I am a postdoctoral fellow in the Geometry and Mathematical Physics group, at SISSA, Trieste. We find that that the smallest singular value of submatrices is related to the minimal distance of points to the lines connecting other two points in a bounded point set. Follow. March 17, 2016 by Louis Y. Liu Leave a comment. Dr. Yang Liu, an Assistant Professor of Mathematics, received his Ph.D. in Mathematics from the University of Georgia in the U.S. and previously his M.S.
In September 2018, I started a PhD at Stanford University in mathematics, and am advised by Aaron Sidford. Photo: Research.
… We appreciate your financial support. Dissertation/Thesis Title: Non-Convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements. Pursue a degree in the fields of Finanical, Pure, Applied, …
), Written Qualifying Examination Study Guide, Past Mathematics Department Award Winners, Placement Criteria for Entry-Level Mathematics Courses at UGA. In this paper, we study the ranges of (absolute value) cosine trans- forms for which we give a proof for an extended surjectivity t heorem by mak- ing applications of the Fredholm’s theorem in integral equa tions, and show a Hermitian characterization theorem for complex Minkowsk i metrics on . One might also be able to put a measure on for the complex norm , , which can be written in real norm as . Your gift is important to us and helps support critical opportunities for students and faculty alike, including lectures, travel support, and any number of educational events that augment the classroom experience. Yang Liu. This is the academic homepage of Yang Liu (I publish under Yang P. Liu). I received my Ph.D. in 2015 from the Ohio State University, Columbus under the supervision of Henri Moscovici. Before attending Stanford, I graduated from MIT in May 2018.
Mainly, using analytical techniques, we show the probabilist ic estimate, precisely, the decay, on the upper tail probability of the larges t strictly convex singular values, when the number of rows of the mat rices becomes very large and the lower tail probability of theirs as well. Click here to learn more about giving. Also, we show some numerical experiential results, which verify the theoretical results.
Moreover, we parametrize the Grassmannian in an elementary linear algebra approach, and give a characterization on the image of the (ab solute value) co- sine transform on the space of distributions on the Grassman nian , by computing the coefficients in the Legendre series expansion o f distributions.
We know that , for any , can be expressed as an integral on by spreading a measure on it, which is. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices, On the Decay of the Smallest Singular Value of Submatrices of Rectangular Matrices, On the Range of Cosine Transform of Distributions for Torus-invariant Complex Minkowski Spaces, THE PROBABILISTIC ESTIMATES ON THE LARGEST AND SMALLEST q-SINGULAR VALUES OF RANDOM MATRICES.
This is the academic homepage of Yang Liu (I publish under Yang P. Liu). About Me. But in the complex case the double integral on the torus.
Research Interests .
2014, 2015 International Math Olympiad gold medal and first-place team, Department of Mathematics Every dollar given has a direct impact upon our students and faculty. In this paper, the p -singular values of random matrices with Gaussian entries defined in terms of the l p -p -norm for p> 1, as is studied. In September 2018, I started a PhD at Stanford University in mathematics, and am advised by Aaron Sidford.
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