Photo by hush52 from unsplash
What is the probability that a needle dropped at random on a set of points scattered on a line segment does not fall on any of them? We compute the… Click to show full abstract
What is the probability that a needle dropped at random on a set of points scattered on a line segment does not fall on any of them? We compute the exact scaling expression of this hole probability when the spacings between the points are independent identically distributed random variables with a power-law distribution of index less than unity, implying that the average spacing diverges. The theoretical framework for such a setting is renewal theory, to which the present study brings a new contribution. The question posed here is also related to the study of some correlation functions of simple models of statistical physics.
Journal Title: Journal of Statistical Mechanics: Theory and Experiment
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!