First-Passage Resetting and its Application to Optimization and to Wealth Sharing

When does a diffusing particle first reach a specified location? This question is answered by the first-passage probability. First-passage ideas underlie diverse phenomena, such as the triggering of integrate-and-fire neurons in the brain to the execution of stock options. In this talk, I'll first present basic facts about first-passage processes.  Then I'll discuss the notion of first-passage resetting, in which a diffusing particle is reset to its starting point whenever a given threshold is first reached.  Finally, I'll present applications of these ideas to optimization in a toy mechanical system and to a simple model of wealth sharing.

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