Analysis of the Jante’s Law Process and Proof of Conjecture: Acknowledgements and References

:::info Authors:

(1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK;

(2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden.

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Abstract and Introduction

Preliminaries

Reduction to the case of uniform geometry

All original points are eventually removed, a. s.

Proof of Theorem 1

Coupling Y (⋅) and Z(⋅)

Acknowledgements and References

Appendix

The research of S.V. is partially supported by the Swedish Science Foundation grant VR 2019- 04173 and the Crafoord Foundation grant no. 20190667. S.V. would like to acknowledge the hospitality of the University of Bristol during his visits to Bristol. The research of E.C. is supported by the Heilbronn Institute for Mathematical Research. We would like to thank John Mackay for pointing us to the notion of uniform geometry in [7] and Rami Atar for pointing out the relevant Brownian bees model. Finally, we would like to thank the anonymous referee for many useful comments and recommendations, in particular the suggestion to explain what can be done in the non-convex case.

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