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Thick points of 4D critical branching Brownian motion

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Thick points show a second-order transition between exponential and stretched exponential phases at the critical dimension.
We determine a critical exponent that governs the probability of hitting distant unit balls in critical branching brownian motion.
Our findings relate thick points to a boundary value problem linked to non-positive solutions of semi-linear PDEs.
The results include an infinite-order asymptotic expansion, which is convergent for certain dimensions and divergent for others.

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Analysis reveals critical dimensions influencing thick point behavior in branching brownian motion, highlighting phase transitions.

Berestycki et al. (2025) studied this question.

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