On the singularity probability of discrete random matrices

Mathematics – Combinatorics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

45 pages, two figures

Scientific paper

Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best upper bound of $(3/4 + o(1))^n$ proven by Tao and Vu in arXiv:math/0501313v2. This paper follows a similar approach to the Tao and Vu result, including using a variant of their structure theorem. We also extend this type of exponential upper bound on the probability that a random matrix is singular to a large class of discrete random matrices taking values in the complex numbers, where the entries are independent but are not necessarily identically distributed.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On the singularity probability of discrete random matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the singularity probability of discrete random matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the singularity probability of discrete random matrices will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-200116

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.