Lower Bound for Large Local Transversal Fluctuations of Geodesics in Last Passage Percolation

Pranay Agarwal ()
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Pranay Agarwal: University of Toronto

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-11

Abstract: Abstract For exactly solvable models of planar last passage percolation, it is known that geodesics of length n exhibit transversal fluctuations at scale $$n^{2/3}$$ n 2 / 3 and matching (up to exponents) upper and lower bounds for the tail probabilities are available. The local transversal fluctuations near the endpoints are expected to be much smaller; it is known that the transversal fluctuation up to distance $$r \ll n$$ r ≪ n is typically of the order $$r^{2/3}$$ r 2 / 3 and the probability that the fluctuation is larger than $$tr^{2/3}$$ t r 2 / 3 is at most $$Ce^{-c{t}^3}$$ C e - c t 3 . In this note, we provide a short argument establishing a matching lower bound for this probability.

Keywords: Last passage percolation; Geodesic; Fluctuation exponent; Kardar–Parisi–Zhang universality; 60K35; 60K37 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01384-8

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