Under independence and tail conditions on random symmetric matrices, the DNN relaxation of the standard quadratic program is exact with probability tending to 1, the optimizer is unique and rank one, and recoverable in O(n^2) time.
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For polynomially mixing billiards with cusps, Birkhoff sums of observables φ(x) = d(x,x0)^{-2/α} with tail index α satisfy stable laws whose index is a function of both α and the mixing exponent γ when γ ∈ (1/2,1) and α ∈ (0,2) excluding 1.
A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.
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Exactness of the DNN Relaxation for Random Standard Quadratic Programs
Under independence and tail conditions on random symmetric matrices, the DNN relaxation of the standard quadratic program is exact with probability tending to 1, the optimizer is unique and rank one, and recoverable in O(n^2) time.
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Stable laws for heavy-tailed observables on polynomially mixing billiards
For polynomially mixing billiards with cusps, Birkhoff sums of observables φ(x) = d(x,x0)^{-2/α} with tail index α satisfy stable laws whose index is a function of both α and the mixing exponent γ when γ ∈ (1/2,1) and α ∈ (0,2) excluding 1.
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Profit Maximization in Bilateral Trade against a Smooth Adversary
A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.