We study survival time statistics in a noisy sample space reducing (SSR)process. Our simulations suggest that both the mean and standard deviationscale as $\sim N/N^{\lambda}$, where $N$ is the system size and $\lambda$ is atunable parameter that characterizes the process. The survival timedistribution has the form $\mathcal{P}_{N}(\tau)\simN^{-\theta}J(\tau/N^{\theta})$, where $J$ is a universal scaling function and$\theta = 1-\lambda$. Analytical insight is provided by a conjecture for theequivalence between the survival time statistics in the noisy SSR process andthe record statistics in a correlated time series modeled as drifted randomwalk with Cauchy distributed jumps.
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机译：我们研究在噪声样本空间减少（SSR）过程中的生存时间统计。我们的模拟表明，均值和标准差标度均为$ \ sim N / N ^ {\ lambda} $，其中$ N $是系统大小，而$ \ lambda $是表征过程的不可取的参数。生存时间分布的格式为$ \ mathcal {P} _ {N}（\ tau）\ simN ^ {-\ theta} J（\ tau / N ^ {\ theta}）$，其中$ J $是通用标度函数和$ \ theta = 1- \ lambda $。通过推测，可以对嘈杂的SSR过程中的生存时间统计数据与相关时间序列中的记录统计数据之间的等价性进行猜想，该相关时间序列建模为具有柯西分布跳跃的漂移随机游走。
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