Esaim-Probability and Statistics最新文献_第4页

A moderate deviation principle for stochastic Hamiltonian systems 随机哈密顿系统的中等偏差原理

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2023-04-04 DOI: 10.1051/ps/2023009

Jie Xu, Jiayin Gong, Jie Ren

引用次数: 1

Strong stationary times for finite Heisenberg walk 有限海森堡行走的强静止时间

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-29 DOI: 10.1051/ps/2023008

L. Miclo

{"title":"Strong stationary times for finite Heisenberg walk","authors":"L. Miclo","doi":"10.1051/ps/2023008","DOIUrl":"https://doi.org/10.1051/ps/2023008","url":null,"abstract":"The random mapping construction of strong stationary times is applied here to finite Heisenberg random walks over $ZZ_M$, for odd $Mgeq 3$.\u0000When they correspond to $3times 3$ matrices, the strong stationary times are of order $M^6$, estimate which can be improved to $M^4$\u0000if we are only interested in the convergence to equilibrium of the last column.\u0000Simulations by Chhaïbi suggest that the proposed strong stationary time is of the right $M^2$ order.\u0000These results are extended to $Ntimes N$ matrices, with $Ngeq 3$.\u0000All the obtained bounds are thought to be non-optimal, nevertheless this original approach is promising, as it relates the investigation of the previously elusive strong stationary times\u0000of such random walks to new absorbing Markov chains with a statistical physics flavor and whose quantitative study is to be pushed further.\u0000In addition, for $N=3$, a strong equilibrium time is proposed in the same spirit for the non-Markovian coordinate in the upper right corner.\u0000This result would extend to separation discrepancy the corresponding fast convergence for this coordinate in total variation\u0000and open a new method for the investigation of this phenomenon in higher dimension.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"56 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80209737","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}

引用次数: 0

Convergence of a scheme for an elastic flow with tangential mesh movement 网格切向运动弹性流格式的收敛性

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022091

Paola Pozzi, Bjoern Stinner

引用次数: 2

Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source 带狄拉克线源的椭圆型和抛物型问题的不连续伽辽金近似

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022095

Rami Masri, Boqian Shen, Beatrice Riviere

引用次数: 0

Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise 带有乘性噪声的随机Maxwell方程的不连续Galerkin方法

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022084

Jiawei Sun, Chi-Wang Shu, Yulong Xing

引用次数: 1

Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow 随机全变分流的概率弱解和强解的数值逼近

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022089

Lubomir Banas, Martin Ondrejat

引用次数: 0

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation 半线性Klein-Gordon方程Lie分裂的二阶低正则性修正

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022096

Buyang Li, Katharina Schratz, Franco Zivcovich

{"title":"A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation","authors":"Buyang Li, Katharina Schratz, Franco Zivcovich","doi":"10.1051/m2an/2022096","DOIUrl":"https://doi.org/10.1051/m2an/2022096","url":null,"abstract":"The numerical approximation of nonsmooth solutions of the semilinear Klein–Gordon equation in the d -dimensional space, with d = 1, 2, 3, is studied based on the discovery of a new cancellation structure in the equation. This cancellation structure allows us to construct a low-regularity correction of the Lie splitting method ( i.e. , exponential Euler method), which can significantly improve the accuracy of the numerical solutions under low-regularity conditions compared with other second-order methods. In particular, the proposed time-stepping method can have second-order convergence in the energy space under the regularity condition $ (u,{mathrm{partial }}_tu)in {L}^{mathrm{infty }}(0,T;{H}^{1+frac{d}{4}}times {H}^{frac{d}{4}})$ . In one dimension, the proposed method is shown to have almost $ frac{4}{3}$ -order convergence in L ∞ (0, T; H 1 × L 2 ) for solutions in the same space, i.e. , no additional regularity in the solution is required. Rigorous error estimates are presented for a fully discrete spectral method with the proposed low-regularity time-stepping scheme. The numerical experiments show that the proposed time-stepping method is much more accurate than previously proposed methods for approximating the time dynamics of nonsmooth solutions of the semilinear Klein–Gordon equation.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"347 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136156906","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}

引用次数: 0

Homogenization of sound-soft and high-contrast acoustic metamaterials in subcritical regimes 亚临界状态下声软和高对比度声学超材料的均匀化

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2022098

Florian Feppon, H. Ammari

{"title":"Homogenization of sound-soft and high-contrast acoustic metamaterials in subcritical regimes","authors":"Florian Feppon, H. Ammari","doi":"10.1051/m2an/2022098","DOIUrl":"https://doi.org/10.1051/m2an/2022098","url":null,"abstract":"We propose a quantitative effective medium theory for two types of acoustic metamaterials constituted of a large number N of small heterogeneities of characteristic size s , randomly and independently distributed in a bounded domain. We first consider a “sound-soft” material, in which the total wave field satisfies a Dirichlet boundary condition on the acoustic obstacles. In the “sub-critical” regime sN = O (1), we obtain that the effective medium is governed by a dissipative Lippmann–Schwinger equation which approximates the total field with a relative mean-square error of order O (max(( sN ) 2 N -1/3, N -1/2)). We retrieve the critical size s ~ 1/ N of the literature at which the effects of the obstacles can be modelled by a “strange term” added to the Helmholtz equation. Second, we consider high-contrast acoustic metamaterials, in which each of the N heterogeneities are packets of K inclusions filled with a material of density much lower than the one of the background medium. As the contrast parameter vanishes, δ → 0, the effective medium admits K resonant characteristic sizes ( s i ( δ )) 1≤ i ≤ K and is governed by a Lippmann–Schwinger equation, which is diffusive or dispersive (with negative refractive index) for frequencies ω respectively slightly larger or slightly smaller than the corresponding K resonant frequencies ( ω i ( δ )) 1≤ i ≤ K . These conclusions are obtained under the condition that (i) the resonance is of monopole type, and (ii) lies in the “subcritical regime” where the contrast parameter is small enough, i.e. δ = o ( N −2 )), while the considered frequency is “not too close” to the resonance, i.e. N δ 1/2 = O (|1 - s/s i (δ)|). Our mathematical analysis and the current literature allow us to conjecture that “solidification” phenomena are expected to occur in the “super-critical” regime N δ 1/2 |1 - s/s i (δ)| -1 → + ∞.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135742588","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}

引用次数: 2

Extensions of Active Flux to arbitrary order of accuracy 将有源通量扩展到任意精度

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2023004

Rémi Abgrall, Wasilij Barsukow

引用次数: 1

On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes 强保稳修正Patankar-Runge-Kutta方案的稳定性

4区数学

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI: 10.1051/m2an/2023005

Juntao Huang, Thomas Izgin, Stefan Kopecz, Andreas Meister, Chi-Wang Shu

引用次数: 3