Thammarat Aree, Charles J McMonagle, Adam A L Michalchuk, Dmitry Chernyshov
{"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}
{"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
{"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}
{"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}
{"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}
{"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}
{"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}