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تسجيل مستخدم جديدSingularity of random integer matrices with large entries
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نشر من قبل
Sankeerth Rao Karingula
تاريخ النشر
2020
مجال البحث
الهندسة المعلوماتية
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English
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We study the singularity probability of random integer matrices. Concretely, the probability that a random $n times n$ matrix, with integer entries chosen uniformly from ${-m,ldots,m}$, is singular. This problem has been well studied in two regimes: large $n$ and constant $m$; or large $m$ and constant $n$. In this paper, we extend previous techniques to handle the regime where both $n,m$ are large. We show that the probability that such a matrix is singular is $m^{-cn}$ for some absolute constant $c>0$. We also provide some connections of our result to coding theory.
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