For random two-component grid diagrams, the odd moments of the linking number vanish, the even moments are polynomials in the grid size, and the normalized linking number converges weakly.
Durrett, Probability: Theory and Examples, 5th edition, Cambridge Series in Statistical and Probabilistic Mathematics
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Linking number of grid models
For random two-component grid diagrams, the odd moments of the linking number vanish, the even moments are polynomials in the grid size, and the normalized linking number converges weakly.