تقرير
Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action
| العنوان: | Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action |
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| المؤلفون: | Pramanik, Paramahansa, Polansky, Alan M. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Primary: 60H05, Secondary: 81Q30 |
| الوصف: | In this paper we present a new theoretical model to find out an optimal weight associated with a soccer player under the presence of a stochastic goal dynamics by using Feynman path integral method, where the action of a player is on $\sqrt{8/3}$-Liouville Quantum Gravity surface. Before determine the optimal weight we first establish an Infinitary logic which can deal with infinite variables on the strategy space then, a quantum formula of this logic has been developed and finally, based on this we are able show the existence of a Lefschetz-Hopf fixed point of this game. As in a competitive tournament, all possible standard strategies to score goals are known to the opposition team, a player's action is stochastic in nature and they would have some comparative advantage to score goals. Furthermore, conditions like uncertainties due to rain, dribbling and passing skill of a player, whether the match is a day match or a day-night match, advantages of having home crowd and asymmetric information of action profiles have been considered on the way to determine the optimal weight. Comment: 32 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.00845 |
| رقم الأكسشن: | edsarx.2108.00845 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |