Shape transition under excess self-intersections for transient random walk
classification
🧮 math.PR
math-phmath.MP
keywords
excesslocalnormrandomshapetimestransienttransition
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We reveal a shape transition for a transient simple random walk forced to realize an excess $q$-norm of the local times, as the parameter $q$ crosses the value $q_c(d)=\frac{d}{d-2}$. Also, as an application of our approach, we establish a central limit theorem for the $q$-norm of the local times in dimension 4 or more.
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