I am a beginner in this field. While I am reading papers and the understanding is getting better. However can someone explain in easy and simple words.
Really thankful !
The probability that a single fluorophore molecule will have a particular off lifetime decreases in direct proportion to the lifetime raised to an exponent (power). This results in a distribution that has a lot of elements with short lifetimes and very few elements with very long lifetimes. When the probability is graphed against the logarithm of lifetime, a straight line results with a negative slope. The slope of the line gives the value of the exponent. To be sure that the relationship is truly a power law distribution, it is important to collect lifetimes over several orders of magnitude.
Article Power‐Law Blinking in the Fluorescence of Single Organic Molecules
Power law statistics in single particle blinking dynamics simply indicates a widely distributed rate process. Please have a look at Article Nearly Suppressed Photoluminescence Blinking of Small Sized,...
Adam B Shapiro Thank you. It was helpful, the paper is also informative.
If I can add anything, it would be some interesting properties of power law statistics. For instance, most power laws have no well defined variance (that is, the variance calculation over the whole distribution does not converge to a finite value). For blinking off times, that would mean there is a variety of them without a clear value of their dispersion. For statistics with clear dispersion/variance values you can say that a very long off time is probable or improbable to a given extent, but for some power law distributions? Think about an endless measurement of blinking of a single particle with such power law blinking statistics - how long a measurement time would be required to sample enough events to provide a histogram of off times that converged to the underlying power law distribution?
There are other interesting features, such as scale invariance.
To continue, this feature is also true for the mean off time for some power law distribution cases. That is, the time average of off times of a single emitter taken for an infinite time diverges, and hence might not be equal to the ensemble average of an infinite number of emitters, or in other words leads to weak ergodicity breaking.
Read more about power-law statistics of single emitters in this Sci News report: https://pubs.aip.org/physicstoday/article/62/2/34/399157/Beyond-quantum-jumps-Blinking-nanoscale-light
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