Geometric max stability of random vectors

Autoregressive Gaussian Random Vectors of First Order

Estimation of Spectral Measure of Stable Random Vectors

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autoregressive gaussian random vectors of first order

Random Max 2-sat and Max Cut

Given a 2-SAT formula F consisting of n variables and b n random clauses, what is the largest number of clauses maxF satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of 34 n and n. We prove that for < 1, the expected number of clauses satisfiable is b n o(1); for large , it is ( 34 + (p ))n; for = 1 + ", it is at least (1 + " O("3))n and at m...

Entanglement of random vectors

We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size and for arbitrary bipartite splitting as an implicit function of index i. Submitted to: J. Phys. A: Math. Gen. PACS numbers: 03.65.Ud, 03.67.-a Entanglement is...