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17 May 2022 The proving of three dimensions in the P´olya’s random walk problem
Jiawei Chen, Zichen Hu, Zhen Liu, Yaocheng Zhan
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Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 122590T (2022) https://doi.org/10.1117/12.2639445
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 2022, Kunming, China
Abstract
Polya’s Random Walk Theorem is a particularly classical and interesting result and also opens the door for many other discussions of probability and statistics problem. This paper aims to present readers with simple cases of Polya’s Random Walk and provide a proof of Random Walk Theorem in d_i (i=1,2,3) based on direct counting method, getting the result of it’s recurrent in d_i (i=1,2) and transient in d_3. This paper states the background of the theorem in a very clear way, which makes the paper more scientific and reliable. The paper also contains some of the literature reviews showing the rigorous attitude of the authors towards science. The main part of this paper consists of the proving process of the three individual dimensions of the Polya’s random walk theorem, in which the authors use precises formulas and calculations to prove the recurrence of Polya’s random walk theorem. At last, the authors present Law of Large Numbers, the first concept of limit theorem, and give the proof of Markov’s Law of Large Numbers, in order to prove the availability of the proving process of the three dimensions, which makes the paper more well-founded.
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Jiawei Chen, Zichen Hu, Zhen Liu, and Yaocheng Zhan "The proving of three dimensions in the P´olya’s random walk problem", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 122590T (17 May 2022); https://doi.org/10.1117/12.2639445
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KEYWORDS
3D modeling
Probability theory
Calculus
Computer science
Tin
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