Pub Date : 2022-06-01Epub Date: 2022-05-11DOI: 10.1107/S2052520622002700
Thammarat Aree, Charles J McMonagle, Adam A L Michalchuk, Dmitry Chernyshov
Highly anharmonic thermal vibrations may serve as a source of structural instabilities resulting in phase transitions, chemical reactions and even the mechanical disintegration of a material. Ab initio calculations model thermal motion within a harmonic or sometimes quasi-harmonic approximation and must be complimented by experimental data on temperature-dependent vibrational frequencies. Here multi-temperature atomic displacement parameters (ADPs), derived from a single-crystal synchrotron diffraction experiment, are used to characterize low-frequency lattice vibrations in the α-FOX-7 layered structure. It is shown that despite the limited quality of the data, the extracted frequencies are reasonably close to those derived from inelastic scattering, Raman measurements and density functional theory (DFT) calculations. Vibrational anharmonicity is parameterized by the Grüneisen parameters, which are found to be very different for in-layer and out-of-layer vibrations.
高非谐波热振动可能是导致相变、化学反应甚至材料机械解体的结构不稳定源。Ab initio 计算是在谐波或有时是准谐波近似范围内建立热运动模型的，必须辅以有关随温度变化的振动频率的实验数据。本文利用单晶同步辐射衍射实验得出的多温度原子位移参数（ADP）来描述 α-FOX-7 层状结构中的低频晶格振动。结果表明，尽管数据质量有限，但提取的频率与非弹性散射、拉曼测量和密度泛函理论（DFT）计算得出的频率相当接近。振动非谐波性是通过格吕尼森参数进行参数化的，发现层内振动和层外振动的格吕尼森参数非常不同。
{"title":"Low-frequency lattice vibrations from atomic displacement parameters of α-FOX-7, a high energy density material.","authors":"Thammarat Aree, Charles J McMonagle, Adam A L Michalchuk, Dmitry Chernyshov","doi":"10.1107/S2052520622002700","DOIUrl":"10.1107/S2052520622002700","url":null,"abstract":"<p><p>Highly anharmonic thermal vibrations may serve as a source of structural instabilities resulting in phase transitions, chemical reactions and even the mechanical disintegration of a material. Ab initio calculations model thermal motion within a harmonic or sometimes quasi-harmonic approximation and must be complimented by experimental data on temperature-dependent vibrational frequencies. Here multi-temperature atomic displacement parameters (ADPs), derived from a single-crystal synchrotron diffraction experiment, are used to characterize low-frequency lattice vibrations in the α-FOX-7 layered structure. It is shown that despite the limited quality of the data, the extracted frequencies are reasonably close to those derived from inelastic scattering, Raman measurements and density functional theory (DFT) calculations. Vibrational anharmonicity is parameterized by the Grüneisen parameters, which are found to be very different for in-layer and out-of-layer vibrations.</p>","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"8 1","pages":"376-384"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9254589/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90932854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We correct typographical errors in our original paper.
摘要我们更正原论文中的印刷错误。
{"title":"On a random search tree: asymptotic enumeration of vertices by distance from leaves – CORRIGENDUM","authors":"M. Bóna, B. Pittel","doi":"10.1017/apr.2021.42","DOIUrl":"https://doi.org/10.1017/apr.2021.42","url":null,"abstract":"Abstract We correct typographical errors in our original paper.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"54 1","pages":"337 - 339"},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44328393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christopher Blier-Wong, Hélène Cossette, É. Marceau
Copulas provide a powerful and flexible tool for modeling the dependence structure of random vectors, and they have many applications in finance, insurance, engineering, hydrology, and other fields. One well-known class of copulas in two dimensions is the Farlie–Gumbel–Morgenstern (FGM) copula, since its simple analytic shape enables closed-form solutions to many problems in applied probability. However, the classical definition of the high-dimensional FGM copula does not enable a straightforward understanding of the effect of the copula parameters on the dependence, nor a geometric understanding of their admissible range. We circumvent this issue by analyzing the FGM copula from a probabilistic approach based on multivariate Bernoulli distributions. This paper examines high-dimensional exchangeable FGM copulas, a subclass of FGM copulas. We show that the dependence parameters of exchangeable FGM copulas can be expressed as a convex hull of a finite number of extreme points. We also leverage the probabilistic interpretation to develop efficient sampling and estimating procedures and provide a simulation study. Throughout, we discover geometric interpretations of the copula parameters that assist one in decoding the dependence of high-dimensional exchangeable FGM copulas.
{"title":"Exchangeable FGM copulas","authors":"Christopher Blier-Wong, Hélène Cossette, É. Marceau","doi":"10.1017/apr.2023.19","DOIUrl":"https://doi.org/10.1017/apr.2023.19","url":null,"abstract":"\u0000 Copulas provide a powerful and flexible tool for modeling the dependence structure of random vectors, and they have many applications in finance, insurance, engineering, hydrology, and other fields. One well-known class of copulas in two dimensions is the Farlie–Gumbel–Morgenstern (FGM) copula, since its simple analytic shape enables closed-form solutions to many problems in applied probability. However, the classical definition of the high-dimensional FGM copula does not enable a straightforward understanding of the effect of the copula parameters on the dependence, nor a geometric understanding of their admissible range. We circumvent this issue by analyzing the FGM copula from a probabilistic approach based on multivariate Bernoulli distributions. This paper examines high-dimensional exchangeable FGM copulas, a subclass of FGM copulas. We show that the dependence parameters of exchangeable FGM copulas can be expressed as a convex hull of a finite number of extreme points. We also leverage the probabilistic interpretation to develop efficient sampling and estimating procedures and provide a simulation study. Throughout, we discover geometric interpretations of the copula parameters that assist one in decoding the dependence of high-dimensional exchangeable FGM copulas.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49348097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract For the gambler’s ruin problem with two players starting with the same amount of money, we show the playing time is stochastically maximized when the games are fair.
摘要对于两个玩家以相同金额开始的赌徒破产问题，我们证明了在游戏公平的情况下，游戏时间是随机最大的。
{"title":"Fair gambler’s ruin stochastically maximizes playing time","authors":"E. Peköz, S. Ross","doi":"10.1017/apr.2021.46","DOIUrl":"https://doi.org/10.1017/apr.2021.46","url":null,"abstract":"Abstract For the gambler’s ruin problem with two players starting with the same amount of money, we show the playing time is stochastically maximized when the games are fair.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"54 1","pages":"656 - 659"},"PeriodicalIF":1.2,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44048455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the large-volume asymptotics of the sum of power-weighted edge lengths $sum_{e in E}|e|^alpha$ in Poisson-based spatial random networks. In the regime $alpha > d$ , we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable $beta$ -skeletons.
研究了基于泊松的空间随机网络中幂加权边长度和$sum_{e in E}|e|^alpha$的大体积渐近性。在$alpha > d$状态下，我们提供了一组充分条件，在这些条件下，上大偏差渐近特征为凝结现象，这意味着过量是由泊松点的可忽略部分引起的。此外，速率函数可以通过一个具体的优化问题来表示。该框架特别包含k-最近邻图的有向、双向和无向变体，以及合适的$beta$ -骨架。
{"title":"Upper large deviations for power-weighted edge lengths in spatial random networks","authors":"C. Hirsch, Daniel Willhalm","doi":"10.1017/apr.2023.10","DOIUrl":"https://doi.org/10.1017/apr.2023.10","url":null,"abstract":"\u0000 We study the large-volume asymptotics of the sum of power-weighted edge lengths \u0000 \u0000 \u0000 \u0000$sum_{e in E}|e|^alpha$\u0000\u0000 \u0000 in Poisson-based spatial random networks. In the regime \u0000 \u0000 \u0000 \u0000$alpha > d$\u0000\u0000 \u0000 , we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable \u0000 \u0000 \u0000 \u0000$beta$\u0000\u0000 \u0000 -skeletons.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46853108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let $(Z_n)_{ngeq 0}$ be a critical branching process in a random environment defined by a Markov chain $(X_n)_{ngeq 0}$ with values in a finite state space $mathbb{X}$ . Let $ S_n = sum_{k=1}^n ln f_{X_k}^{prime}(1)$ be the Markov walk associated to $(X_n)_{ngeq 0}$ , where $f_i$ is the offspring generating function when the environment is $i in mathbb{X}$ . Conditioned on the event ${ Z_n>0}$ , we show the nondegeneracy of the limit law of the normalized number of particles ${Z_n}/{e^{S_n}}$ and determine the limit of the law of $frac{S_n}{sqrt{n}} $ jointly with $X_n$ . Based on these results we establish a Yaglom-type theorem which specifies the limit of the joint law of $ log Z_n$ and $X_n$ given $Z_n>0$ .
{"title":"Limit theorems for critical branching processes in a finite-state-space Markovian environment","authors":"I. Grama, Ronan Lauvergnat, Émile Le Page","doi":"10.1017/apr.2021.18","DOIUrl":"https://doi.org/10.1017/apr.2021.18","url":null,"abstract":"Abstract Let \u0000$(Z_n)_{ngeq 0}$\u0000 be a critical branching process in a random environment defined by a Markov chain \u0000$(X_n)_{ngeq 0}$\u0000 with values in a finite state space \u0000$mathbb{X}$\u0000 . Let \u0000$ S_n = sum_{k=1}^n ln f_{X_k}^{prime}(1)$\u0000 be the Markov walk associated to \u0000$(X_n)_{ngeq 0}$\u0000 , where \u0000$f_i$\u0000 is the offspring generating function when the environment is \u0000$i in mathbb{X}$\u0000 . Conditioned on the event \u0000${ Z_n>0}$\u0000 , we show the nondegeneracy of the limit law of the normalized number of particles \u0000${Z_n}/{e^{S_n}}$\u0000 and determine the limit of the law of \u0000$frac{S_n}{sqrt{n}} $\u0000 jointly with \u0000$X_n$\u0000 . Based on these results we establish a Yaglom-type theorem which specifies the limit of the joint law of \u0000$ log Z_n$\u0000 and \u0000$X_n$\u0000 given \u0000$Z_n>0$\u0000 .","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"54 1","pages":"111 - 140"},"PeriodicalIF":1.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49036361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Using one-dimensional branching Brownian motion in a periodic environment, we give probabilistic proofs of the asymptotics and uniqueness of pulsating traveling waves of the Fisher–Kolmogorov–Petrovskii–Piskounov (F-KPP) equation in a periodic environment. This paper is a sequel to ‘Branching Brownian motion in a periodic environment and existence of pulsating travelling waves’ (Ren et al., 2022), in which we proved the existence of the pulsating traveling waves in the supercritical and critical cases, using the limits of the additive and derivative martingales of branching Brownian motion in a periodic environment.
摘要利用周期环境中的一维分支布朗运动，给出了周期环境中Fisher–Kolmogorov–Petrovskii–Piskounov（F-KPP）方程脉动行波的渐近性和唯一性的概率证明。本文是“周期环境中的分支布朗运动和脉动行波的存在”（Ren et al.，2022）的续篇，其中我们利用周期环境中分支布朗运动的加性和导数鞅的极限，证明了在超临界和临界情况下脉动行波的存在。
{"title":"Branching Brownian motion in a periodic environment and uniqueness of pulsating traveling waves","authors":"Yanxia Ren, R. Song, Fan Yang","doi":"10.1017/apr.2022.32","DOIUrl":"https://doi.org/10.1017/apr.2022.32","url":null,"abstract":"Abstract Using one-dimensional branching Brownian motion in a periodic environment, we give probabilistic proofs of the asymptotics and uniqueness of pulsating traveling waves of the Fisher–Kolmogorov–Petrovskii–Piskounov (F-KPP) equation in a periodic environment. This paper is a sequel to ‘Branching Brownian motion in a periodic environment and existence of pulsating travelling waves’ (Ren et al., 2022), in which we proved the existence of the pulsating traveling waves in the supercritical and critical cases, using the limits of the additive and derivative martingales of branching Brownian motion in a periodic environment.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"55 1","pages":"510 - 548"},"PeriodicalIF":1.2,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46302709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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