English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1independently with probability 1/2. Our main result implies that theprobability 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 Taoand Vu in arXiv:math/0501313v2. This paper follows a similar approach to theTao and Vu result, including using a variant of their structure theorem. Wealso extend this type of exponential upper bound on the probability that arandom matrix is singular to a large class of discrete random matrices takingvalues in the complex numbers, where the entries are independent but are notnecessarily identically distributed.

On the singularity probability of discrete random matrices