Analysis of the Jante’s Law Process and Proof of Conjecture: Proof of Theorem 1

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. Table of Links 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 5 Proof of Theorem 1 Without loss of generality, we assume that the initial state Z(0) is deterministic. This is harmless since if for each deterministic choice of Z(0) the limit z∞ exists a.s. and has an absolutely continuous distribution, then if instead Z(0) is random, z∞ still exists a.s. and its distribution is a mixture of absolutely continuous distributions, which is necessarily absolutely continuous. This paper is available on arxiv under CC 4.0 license. 7 i.e., a set defined by a number of polynomial inequalities and equalities; in our case, a.s. these will be just inequalities. 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. Authors: 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. Table of Links Abstract and Introduction Abstract and Introduction Preliminaries Preliminaries Reduction to the case of uniform geometry Reduction to the case of uniform geometry All original points are eventually removed, a. s. All original points are eventually removed, a. s. Proof of Theorem 1 Proof of Theorem 1 Coupling Y (⋅) and Z(⋅) Coupling Y (⋅) and Z(⋅) Acknowledgements and References Acknowledgements and References Appendix Appendix 5 Proof of Theorem 1 Without loss of generality, we assume that the initial state Z(0) is deterministic. This is harmless since if for each deterministic choice of Z(0) the limit z∞ exists a.s. and has an absolutely continuous distribution, then if instead Z(0) is random, z∞ still exists a.s. and its distribution is a mixture of absolutely continuous distributions, which is necessarily absolutely continuous. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv 7 i.e., a set defined by a number of polynomial inequalities and equalities; in our case, a.s. these will be just inequalities.

Analysis of the Jante’s Law Process and Proof of Conjecture: Proof of Theorem 1

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