Four Dimensions

Part of the Probability and Its Applications book series (PA)


The critical dimension for intersections of two random walks, d = 4, will be studied in this chapter. The critical dimension is characterized by logarithmic behavior of the interesting quantities. The results in this chapter will be stronger than what we can prove in two and three dimensions— instead of just upper and lower bounds for probabilities we will be able to give asymptotic expressions.


Random Walk Indicator Function Critical Dimension Asymptotic Expression Standard Normal Random Variable 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  1. 1.Department of MathematicsDuck UniversityDurhamUSA

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