Random Bridges in Spaces of Growing Dimension

2025/03/17 by Jin, Bochen · 1 citation
#60F05 60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.13132

Abstract

We investigate the limiting behaviour of the path of random bridges treated as random sets in ℝ^d with the Euclidean metric and the dimension d increasing to infinity. The main result states that, in the square integrable case, the limit (in the Gromov-Hausdorff sense) is deterministic, namely, it is [0,1] equipped with the pseudo-metric √(|t-s|(1-|t-s|)). We also show that, in the heavy-tailed case with summands regularly varying of order α∈ (0,1), the limiting metric space has a random metric derived from the bridge variant of a subordinator.

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• Convergence of Random Walks in ℓ_p-Spaces of Growing Dimension

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