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Real eigenvalues of non-Gaussian random matrices and their products
Sajna Hameed, Kavita Jain, Arul Lakshminarayan
We study the properties of the eigenvalues of real random matrices and their products. It is known that when the matrix elements are Gaussian-distributed independent random variabl…
On the number of real eigenvalues of products of random matrices and an application to quantum entanglement
Arul Lakshminarayan
The probability that there are real eigenvalues for an dimensional real random matrix is known. Here we study this for the case of products of independent random matrices.…
Cyclic Identities Involving Ratios of Jacobi Theta Functions
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at equally shifted points were recently found. The purpose of this paper is to re-ex…
Local Identities Involving Jacobi Elliptic Functions
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler d…
Cyclic Identities Involving Jacobi Elliptic Functions. II
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at equally shifted points on the real axis were recently found. These identities pla…