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Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale
Critical Gaussian Multiplicative Chaos Convergence of the Derivative Martingale Probability
2012/6/29
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
Multidimensional semicircular limits on the free Wigner chaos
Convergence in Distribution Fourth Moment Condition Free BrownianMotion Free Probability Multidimensional Limit Theorems
2011/9/21
Abstract: We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This...