How Many Blocks Can Children Pile Up ? - Some Analytical Results -

Abstract

The inverse Gaussian probability density is shown to describe the statistical properties of the height of a pile of blocks in the experiment of Iwasaka and Honda. Our derivation furnishes an elementary analytical result for models exhibiting a self-organized behavior. Moreover, the method we use, based on the first hitting time of a stochastic process to a moving boundary, suggests natural generalizations for more complex systems.