kHz) is low compared with typical microscopic "attempt frequencies" (e.g., 1014 Hz), the exponential factors in the Arrhenius equation for the rates are large. Relatively small spreads in the activation energies appearing in these exponents then result in large spreads of characteristic rates. In the simplest toy case, a flat distribution of activation energies gives exactly a pink spectrum, because There is no known lower bound to background pink noise in electronics. Measurements made down to 10−6 Hz (taking several weeks) have not shown a ceasing of pink-noise behaviour. A pioneering researcher in this field was Aldert van der Ziel. In gravitational wave astronomy 1/f α noises with α near 1 are a factor in gravitational-wave astronomy. The noise curve at very low frequencies affects pulsar timing arrays, the European Pulsar Timing Array (EPTA) and the future International Pulsar Timing Array (IPTA); at low frequencies are space-borne detectors, the formerly proposed Laser Interferometer Space Antenna (LISA) and the currently proposed evolved Laser Interferometer Space Antenna (eLISA), and at high frequencies are ground-based detectors, the initial Laser Interferometer Gravitational-Wave Observatory (LIGO) and its advanced configuration (aLIGO). The characteristic strain of potential astrophysical sources are also shown. To be detectable the characteristic strain of a signal must be above the noise curve. Climate change Pink noise on timescales of decades has been found in climate proxy data, which may indicate amplification and coupling of processes in the climate system. Diffusion processes Many time-dependent stochastic processes are known to exhibit 1/f α noises with α between 0 and 2. In particular Brownian motion has a power spectral density that equals 4D/f 2, where D is the diffusion coefficient. This type of spectrum is sometimes referred to as Brownian noise. Interestingly, the analysis of individual Brownian motion trajectories also show 1/f 2 spectrum, albeit with random amplitudes. Fractional Brownian motion with Hurst exponent H also show 1/f α power spectral density with α=2H+1 for subdiffusive processes (H<0.5) and α=2 for superdiffusive processes (0.5<H<1). Origin There are many theories about the origin of pink noise. Some theories attempt to be universal, while others apply to only a certain type of material, such as semiconductors. Universal theories of pink noise remain a matter of current research interest. A hypothesis (referred to as the Tweedie hypothesis) has been proposed to explain the genesis of pink noise on the basis of a mathematical convergence theorem related to the