英文标题：
《Nucleation, condensation and lambda-transition on a real-life stock
market》
---
作者：
M. Wilinski, B. Szewczak, T. Gubiec, R. Kutner and Z. R. Struzik
---
最新提交年份：
2014
---
英文摘要：
We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex systems by identifying three of them on real-life financial markets. We extract and interpret the empirical, numerical, and semi-analytical evidences for the existence of these phase transitions, by considering the Frankfurt Stock Exchange (FSE), as a typical example of a financial market of a medium size. Using the canonical object for the graph theory, i.e. the Minimal Spanning Tree (MST) network, we observe: (i) The initial phase transition from the equilibrium to non-equilibrium MST network in its nucleation phase, occurring at some critical time. Coalescence of edges on the FSE\'s transient leader is observed within the nucleation and is approximately characterized by the Lifsthiz-Slyozov growth exponent; (ii) The nucleation accelerates and transforms to the condensation process, in the second phase transition, forming a logarithmically diverging lambda-peak of short-range order parameters at the subsequent critical time - an analogon of such a transition in superfluidity; (iii) In the third phase transition, the peak logarithmically decreases over three quarters of the year, resulting in a few loosely connected sub-graphs. This peak is reminiscent of a non-equilibrium superstar-like superhub or a `dragon king\' effect, abruptly accelerating the evolution of the leader company. All these phase transitions are caused by the few richest vertices, which drift towards the leader and provide the most of the edges increasing the leader\'s degree. Thus, we capture an amazing phenomenon, likely of a more universal character, where a peripheral vertex becomes the one which is over dominating the complex network during an exceptionally long period of time.
---
中文摘要：
我们通过在现实金融市场上识别三个复杂系统中的动态相变，填补了将复杂系统中的动态相变的经验和现象学特征结合起来的空白。通过将法兰克福证券交易所（FSE）视为中等规模金融市场的典型例子，我们提取并解释了这些相变存在的经验、数值和半分析证据。利用图论中的典型对象，即最小生成树（MST）网络，我们观察到：（i）从平衡到非平衡的MST网络在其成核阶段的初始相变，发生在某个临界时间。在成核过程中，可以观察到FSE瞬态先导上的边缘合并，其特征近似为Lifsthiz-Slyozov生长指数；（ii）在第二相转变中，成核加速并转变为冷凝过程，在随后的临界时间形成短程序参数的对数发散λ峰——类似于超流体中的这种转变；（iii）在第三阶段转换中，峰值在一年的三个季度内对数下降，导致一些松散连接的子图。这一峰值让人联想到一个非均衡的超级巨星，比如superhub或“龙王”效应，突然加速了领先公司的发展。所有这些相变都是由少数最富有的顶点引起的，这些顶点向引线漂移，并提供了增加引线阶数的大部分边。因此，我们捕捉到了一个惊人的现象，可能是一个更普遍的特征，即一个外围顶点在异常长的时间内成为一个在复杂网络中占据主导地位的顶点。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
--

---
PDF下载：
-->