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

This paper is available on arxiv(https://arxiv.org/abs/2211.15237) under CC 4.0 license. We assume that the initial state Z(0) is deterministic. Without loss of generality, we assume the limit z∞ exists a.s. and has an absolutely continuous distribution.


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:::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.

:::

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.

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:::info This paper is available on arxiv under CC 4.0 license.

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7 i.e., a set defined by a number of polynomial inequalities and equalities; in our case, a.s. these will be just inequalities.

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This content originally appeared on HackerNoon and was authored by Keynesian Technology


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