Under σ-smooth valuation distributions, ε-differentially private α-optimal mechanisms for bilateral trade are learnable with Õ(1/(σ ε α²)) samples for profit and Õ(1/(ε α) + 1/α²) samples for gain-from-trade efficiency.
Asymptotic distributions for the intervals estimators of the ex- tremal index and the cluster-size probabilities
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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.
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.
An automated detection method applied to simulated flare ribbon data identifies fine structures whose motions and flux distribution are consistent with plasmoid-mediated reconnection.
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.
A consistent bias-corrected estimator based on blockwise top-two order statistics is developed for extreme value analysis after showing the naive independence-likelihood approach is inconsistent.
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Private Learning in Bilateral Trade
Under σ-smooth valuation distributions, ε-differentially private α-optimal mechanisms for bilateral trade are learnable with Õ(1/(σ ε α²)) samples for profit and Õ(1/(ε α) + 1/α²) samples for gain-from-trade efficiency.
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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.