Coupling Derivation of Optimal-Order Central Moment Bounds in Exponential Last-Passage Percolation

Area of Science:

• Probability theory
• Stochastic processes
• Statistical physics

Background:

• Planar directed last-passage percolation (p-dLPP) is a key model in statistical physics.
• Understanding moment bounds and fluctuation behavior is crucial for analyzing p-dLPP.
• Existing methods for bounding moments and fluctuations have limitations.

Purpose of the Study:

• To derive optimal-order central moment bounds for p-dLPP.
• To introduce novel probabilistic arguments for analyzing fluctuation bounds.
• To provide a new proof for the left-tail fluctuation upper bound.

Main Methods:

• Utilizing probabilistic arguments.
• Employing couplings with increment-stationary variants of p-dLPP.
• Focusing on models with independent and identically distributed (i.i.d.) exponential weights.
• Considering both zero and near-stationary boundary conditions.

Main Results:

• Successful derivation of optimal-order central moment bounds.
• Development of a new technique based on couplings.
• A novel proof for the left-tail fluctuation upper bound with exponent 3/2 for last-passage times.

Conclusions:

• The new probabilistic approach effectively establishes optimal moment bounds.
• The findings contribute to a deeper theoretical understanding of p-dLPP.
• The novel proof technique offers a significant advancement in analyzing tail fluctuations.