常见的概率模式源于简单不变性
Common probability patterns arise from simple invariances
摘要：
平移和拉伸不变性导致指数玻尔兹曼概率分布。旋转不变性产生高斯分布。特定的标度关系将典型的指数和高斯模式转换为各种常见的观察模式。标度关系本身产生于平移、拉伸和旋转的基本不变性，加上一些额外的不变性。先前的工作描述了三个基本不变性作为结果的平衡正则系综的统计力学或Jaynesian最大化的信息熵。相比之下，我强调不变性本身的首要性和充分性来解释通常观察到的模式。基本不变性自然地创建了一系列常见的尺度关系和相关的概率模式，而从统计力学或信息论导出的经典方法需要特殊的假设来导出常见的尺度。
英文摘要：
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into the variety of commonly observed patterns. The scaling relations themselves arise from the fundamental invariances of shift, stretch, and rotation, plus a few additional invariances. Prior work described the three fundamental invariances as a consequence of the equilibrium canonical ensemble of statistical mechanics or the Jaynesian maximization of information entropy. By contrast, I emphasize the primacy and sufficiency of invariance alone to explain the commonly observed patterns. Primary invariance naturally creates the array of commonly observed scaling relations and associated probability patterns, whereas the classical approaches derived from statistical mechanics or information theory require special assumptions to derive commonly observed scales.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
