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Slowly vanishing memories

Chris Leemann

posted on 24 December 2012

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When a statistical variable has strayed from its mean value, how can we best describe its tendency to return to the equilibrium state ? In a great many instances the expected size of the next step towards equilibrium is proportional to the actual value of the variable. The ensuing relaxation is exponential in time if the probability for a step to occur in a given time interval is constant. If on the other hand this probability increases at least as fast as lineraly with the random variable, the variable is found to have good long term memory.