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Probability-theoretic interpretation of degeneracy locus formulas
Abstract
Schwartz-MacPherson classes of degeneracy loci of symmetric and skew-symmetric maps. Together with the known formulas for ordinary linear maps, this completes the stable SSM theory for the three classical types. We interpret these formulas probabilistically, in terms of the endpoint random partition of a stochastic rational six-vertex model: the skew classes are probabilities of Maya-dimer events, and the symmetric classes are Chebyshev moments of the random 2-core.
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BibTeX
@misc{rimanyi2026probabilitytheoretic,
title = {{Probability-theoretic interpretation of degeneracy locus formulas}},
author = {Richard Rimanyi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06237},
eprint = {2609.06237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06237},
}
RIS
TY - UNPB
TI - Probability-theoretic interpretation of degeneracy locus formulas
AU - Richard Rimanyi
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06237
UR - https://arxiv.org/abs/2609.06237
AB - Schwartz-MacPherson classes of degeneracy loci of symmetric and skew-symmetric maps. Together with the known formulas for ordinary linear maps, this completes the stable SSM theory for the three classical types. We interpret these formulas probabilistically, in terms of the endpoint random partition of a stochastic rational six-vertex model: the skew classes are probabilities of Maya-dimer events, and the symmetric classes are Chebyshev moments of the random 2-core.
ER -