Abstract:We study the long-time behaviour of a coninuous time one-dimensional elephant random walk with an absorbing boundary. By analyzing the associated evolution equation, we identify a proper limiting operator and establish a Poincaré inequality with spectral gap of order $N^{-2}$. As a consequence, we obtain matching exponential upper and lower bounds for the survival probability, showing that it decays at rate $e^{-ct/N^2}$. The proof relies on a decomposition of the generator into a limiting operator and a time-dependent perturbation, together with spectral estimates.
From: Ioannis Papageorgiou [view email]
[v1]
Sun, 7 Jun 2026 23:56:13 UTC (10 KB)
[v2]
Sat, 15 Aug 2026 02:02:31 UTC (11 KB)
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