Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants ͗͗n m ͘͘ of the number n of passed charges to very high orders (up to m ‫؍‬ 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.cumulants ͉ distributions ͉ electron transport ͉ noise and fluctuations C ounting statistics concerns the probability distribution P n of the number n of random events that occur during a certain time span t. One example is the number of electrons that tunnel through a nanoscopic system (1-4). The first cumulant of the distribution is the mean of n, ͗͗n͘͘ ϭ ͗n͘, the second is the variance, ͗͗n 2 ͘͘ ϭ ͗n 2 ͘ Ϫ ͗n͘ 2 , the third is the skewness, ͗͗n 3 ͘͘ ϭ ͗(n Ϫ ͗n͘) 3 ͘. With increasing order the cumulants are expected to contain more and more detailed information on the microscopic correlations that determine the stochastic process. In general, the cumulants ͗͗n m ͘͘ ϭ S (m) (z ϭ 0) are defined as the mth derivative with respect to the counting field z of the cumulant generating function (CGF) S(z) ϭ ln͚ n P n e nz . Recently, theoretical studies of a number of different systems have found that the high-order cumulants oscillate as functions of certain parameters (5-9), however, no systematic explanation of this phenomenon has so far been given. Examples include oscillations of the high-order cumulants of transport through a Mach-Zender interferometer as functions of the Aharonov-Bohm flux (6), and in transport through a double quantum dot as functions of the energy dealignment between the two quantum dots (8). As we shall demonstrate, oscillations of the high-order cumulants in fact constitute a universal phenomenon which is to be expected in a large class of stochastic processes, independently of the microscopic details. Inspired by recent ideas of M. V. Berry for the behavior of high-order derivates of complex functions (10), we show that the high-order cumulants for a large variety of stochastic processes become oscillatory functions of basically any parameter, including time in the transient regime. We develop the theory underlying this surprising phenomenon and present the first...

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