article epub_ahead yes Lawrence Hollom author Lyuben Lichev author 9aa8388e-d003-11ee-8458-c4c1d7447977 Adva Mond author Julien Portier author MaKw department THRESHOLDS IN SEMI-RANDOM PROCESSES AND GRAPH EMBEDDINGS project For a tree T and a function f:E(T)→Sd, the imbalance of a subtree T′⊆T is given by |∑e∈E(T′)f(e)|. The d-dimensional discrepancy of the tree T is the minimum, over all functions f as above, of the maximum imbalance of a subtree of T. We prove tight asymptotic bounds for the discrepancy of a tree T, confirming a conjecture of Krishna, Michaeli, Sarantis, Wang and Wang. We also settle a related conjecture on oriented discrepancy of subtrees by the same authors. Springer2026 eng TreesHigh-dimensional discrepancyOriented discrepancy 0179-5376 1432-0444 2412.0417010.1007/s00454-025-00790-x Hollom L, Lichev L, Mond A, Portier J. A note on high-dimensional discrepancy of subtrees. <i>Discrete and Computational Geometry</i>. 2026. doi:<a href="https://doi.org/10.1007/s00454-025-00790-x">10.1007/s00454-025-00790-x</a> Hollom, Lawrence, et al. “A Note on High-Dimensional Discrepancy of Subtrees.” <i>Discrete and Computational Geometry</i>, Springer, 2026, doi:<a href="https://doi.org/10.1007/s00454-025-00790-x">10.1007/s00454-025-00790-x</a>. Hollom L, Lichev L, Mond A, Portier J. 2026. A note on high-dimensional discrepancy of subtrees. Discrete and Computational Geometry. L. Hollom, L. Lichev, A. Mond, J. Portier, Discrete and Computational Geometry (2026). L. Hollom, L. Lichev, A. Mond, and J. Portier, “A note on high-dimensional discrepancy of subtrees,” <i>Discrete and Computational Geometry</i>. Springer, 2026. Hollom, Lawrence, Lyuben Lichev, Adva Mond, and Julien Portier. “A Note on High-Dimensional Discrepancy of Subtrees.” <i>Discrete and Computational Geometry</i>. Springer, 2026. <a href="https://doi.org/10.1007/s00454-025-00790-x">https://doi.org/10.1007/s00454-025-00790-x</a>. Hollom, L., Lichev, L., Mond, A., &#38; Portier, J. (2026). A note on high-dimensional discrepancy of subtrees. <i>Discrete and Computational Geometry</i>. Springer. <a href="https://doi.org/10.1007/s00454-025-00790-x">https://doi.org/10.1007/s00454-025-00790-x</a> 231582026-10-18T22:01:53Z2026-10-19T08:20:42Z