Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 5: Focus Session: Physics of Behavior (joint session SOE/DY)

DY 5.10: Vortrag

Montag, 9. März 2026, 12:30–12:45, GÖR/0226

Statistical mechanics of connected graphs in Scrabble — •Olivier Witteveen and Marianne Bauer — Department of Bionanoscience, Kavli Institute of Nanoscience Delft, TU Delft, Van der Maasweg 9, 2629 HZ Delft, The Netherlands

The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We are interested in describing the ensemble of these Scrabble graphs and comparing them across different languages. To find the most structureless description of Scrabble graphs, we build a maximum-entropy probability distribution; using real tournament data, we adapt a pseudo-likelihood method to the case of connected graphs on a lattice. We find that a maximum-entropy distribution that includes means and pairwise correlations captures the data: it correctly predicts simultaneous square occupation, word-length statistics, and geometric features of the Scrabble graphs, as well as the hierarchy among square types. Finally, we explore how language affects the structure of the Scrabble graphs. We adapt a Scrabble bot to self-play and generate graphs using different lexica. We find that the graphs produced by the bot have lower entropy compared to human players, and that lexica with shorter words yield higher entropy graphs. Remarkably, the pairwise maximum-entropy distribution is almost sufficient to correctly assign Scrabble graphs to their corresponding lexica.

Keywords: Maximum entropy; Inference; Inverse Ising