Random bridges in spaces of growing dimension

Bochen Jin

Statistics & Probability Letters, 2026, vol. 227, issue C

Abstract: We investigate the limiting behaviour of the path of random bridges treated as random sets in Rd 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.

Keywords: Gromov–Hausdorff distance; Bridge variant random walk; Growing dimension; Metric space (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spl.2025.110530

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