Freezing and Decorated Poisson Point Processes
Freezing and Decorated Poisson Point Processes
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冷冻和装饰泊松点过程
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
O. Zeitouni
中科院分区：
文献类型：
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作者：
Eliran Subag;O. Zeitouni
已知分支布朗运动 (BBM)、双速 BBM 和分支随机游走的极限极值过程是随机平移装饰泊松点过程 (SDPPP)。在这些结果的证明中，对于任何非零、非负、紧支持的连续函数 f，极限极值过程的拉普拉斯泛函满足 $${L\left[\theta_{y}f\right]=g\left(y-\tau_{f}\right)}$$Lθyf=gy-τf，其中 $${\theta_{y}}$$θy 是移位运算符， $${\tau_{f}}$$τf 是依赖于 f 的实数，g 是独立于 f 的实函数。我们表明，在某些假设下，这一属性表征了 SDPPP 的结构。此外，当它成立时，我们证明 g 必须是具有某种度量的 Gumbel 分布的卷积。拉普拉斯泛函的上述性质与“冻结现象”密切相关，这种现象预计会在广泛的对数相关领域中发生，并且在各种模型的分析中发挥了重要作用。我们的结果揭示了这一有趣的现象，并为在这些模型和其他模型中证明 SDPPP 结构提供了一个自然的工具。
The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace functional of the limiting extremal process is shown to satisfy $${L\left[\theta_{y}f\right]=g\left(y-\tau_{f}\right)}$$Lθyf=gy-τf for any nonzero, nonnegative, compactly supported, continuous function f, where $${\theta_{y}}$$θy is the shift operator, $${\tau_{f}}$$τf is a real number that depends on f, and g is a real function that is independent of f. We show that, under some assumptions, this property characterizes the structure of SDPPP. Moreover, when it holds, we show that g has to be a convolution of the Gumbel distribution with some measure.The above property of the Laplace functional is closely related to a ‘freezing phenomenon’ that is expected to occur in a wide class of log-correlated fields, and which has played an important role in the analysis of various models. Our results shed light on this intriguing phenomenon and provide a natural tool for proving an SDPPP structure in these and other models.
影响因子：
2
作者：
L. Arguin;Anton Bovier;N. Kistler
通讯作者：
L. Arguin;Anton Bovier;N. Kistler
计算多重分形模式中的函数波动和极值阈值：理想 1/f 噪声的案例研究
影响因子：
1.6
作者：
Fyodorov Y
通讯作者：
Fyodorov Y