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PreprintCC BY 4.0HAL

Rigidity of one-dimensional point processes via optimal transport

  • David Dereudre
  • Rafaël Digneaux
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Abstract

We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an L1 transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of Number-Rigidity and Cyclic-Factor. We then apply this result to non-singular Riesz gases with parameter s∈(−2,−1], defined in infinite volume as accumulation points of stationarized finite-volume Riesz gases. This includes, for s=−1, the well-known one-dimensional Coulomb gas (also called Jellium plasma, or the one-component 1D plasma).

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Cite

BibTeXRIS
BibTeX
@misc{dereudre2026rigidity,
  title = {{Rigidity of one-dimensional point processes via optimal transport}},
  author = {David Dereudre and Rafaël Digneaux},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  eprint = {2510.17257},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05318149v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Rigidity of one-dimensional point processes via optimal transport
AU  - David Dereudre
AU  - Rafaël Digneaux
PY  - 2026
DA  - 2026/09/18
PB  - HAL
UR  - https://hal.science/hal-05318149v2
AB  - We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an L^1 transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of Number-Rigidity and Cyclic-Factor. We then apply this result to non-singular Riesz gases with parameter s∈(−2,−1], defined in infinite volume as accumulation points of stationarized finite-volume Riesz gases. This includes, for s=−1, the well-known one-dimensional Coulomb gas (also called Jellium plasma, or the one-component 1D plasma).
ER  -