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math.PR2023
Angle between two random segments
Paulo Manrique-Mirón
The study of \textit{random segments} is a classical problem in geometrical probability whose answer depends on the mechanism used to generate the segments. We consider four indepe…
math.PR2023
Condition Number of Random Tridiagonal Toeplitz Matrix
Paulo Manrique-Mirón
In this manuscript it is considered the eigenvalues of a random tridiagonal Toeplitz matrix . We study the asymptotic behavior of the joint distribution of $({|λ|_{\min} ,…
math.PR2019
Angle distribution of two random chords in the disc: A sine law
Jesus Igor Heberto Barahona Torres, Paulo Cesar Manrique-Mirón, Erick Treviño-Aguilar
Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main…