Alea-Latin American Journal of Probability and Mathematical Statistics最新文献_第9页

On the Passage Time Geometry of theLast Passage Percolation Problem 关于最后通道渗流问题的通过时间几何

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-01-01 DOI: 10.30757/alea.v18-10

Tom Alberts, E. Cator

引用次数: 1

On the affine recursion on R_d+ in the critical case 临界情况下R_d+上的仿射递归

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-01-01 DOI: 10.30757/ALEA.V18-37

S. Brofferio, M. Peigné, Thi da Cam Pham

引用次数: 2

Mixing properties of integer-valued GARCH processes 整数值GARCH过程的混合特性

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-01-01 DOI: 10.30757/ALEA.V18-18

P. Doukhan, N. M. Khan, Michael H. Neumann

引用次数: 7

Quantization and martingale couplings 量子化与鞅耦合

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-12-18 DOI: 10.30757/alea.v19-01

B. Jourdain, G. Pagès

{"title":"Quantization and martingale couplings","authors":"B. Jourdain, G. Pagès","doi":"10.30757/alea.v19-01","DOIUrl":"https://doi.org/10.30757/alea.v19-01","url":null,"abstract":"Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly supported, it is smaller than any of its dual quantizations while the dominated original measure is greater than any of its stationary (and therefore any of its quadratic optimal) primal quantization. Moreover, the quantization errors then correspond to martingale couplings between each original probability measure and its quantization. This permits to prove that any martingale coupling between the original probability measures can be approximated by a martingale coupling between their quantizations in Wassertein distance with a rate given by the quantization errors but also in the much finer adapted Wassertein distance. As a consequence, while the stability of (Weak) Martingale Optimal Transport problems with respect to the marginal distributions has only been established in dimension 1 so far, their value function computed numerically for the quantized marginals converges in any dimension to the value for the original probability measures as the numbers of quantization points go to ∞.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49344322","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: 5

Fluctuations of the Magnetization for Ising models on Erdős-Rényi random graphs – the regimes of low temperature and external magnetic field Erdős-Rényi随机图上Ising模型磁化的波动——低温和外磁场的状态

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-12-15 DOI: 10.30757/alea.v19-21

Z. Kabluchko, Matthias Lowe, K. Schubert

引用次数: 4

Undirected Polymers in Random Environment: path properties in the mean field limit. 随机环境中的无向聚合物：平均场极限中的路径性质。

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-12-07 DOI: 10.30757/alea.v19-61

N. Kistler, A. Schertzer

{"title":"Undirected Polymers in Random Environment: path properties in the mean field limit.","authors":"N. Kistler, A. Schertzer","doi":"10.30757/alea.v19-61","DOIUrl":"https://doi.org/10.30757/alea.v19-61","url":null,"abstract":"We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement of the second moment method we obtain a fairly precise geometrical description of optimal paths, i.e. of polymers with minimal energy. The picture which emerges can be loosely summarized as follows. The energy of the polymer is, to first approximation, uniformly spread along the strand. The polymer's bonds carry however a lower energy than in the directed setting, and are reached through the following geometrical evolution. Close to the origin, the polymer proceeds in oriented fashion -- it is thus as stretched as possible. The tension of the strand decreases however gradually, with the polymer allowing for more and more backsteps as it enters the core of the hypercube. Backsteps, although increasing the length of the strand, allow the polymer to connect reservoirs of energetically favorable edges which are otherwise unattainable in a fully directed regime. These reservoirs lie at mesoscopic distance apart, but in virtue of the high dimensional nature of the ambient space, the polymer manages to connect them through approximate geodesics with respect to the Hamming metric: this is the key strategy which leads to an optimal energy/entropy balance. Around halfway, the mirror picture sets in: the polymer tension gradually builds up again, until full orientedness close to the endpoint. The approach yields, as a corollary, a constructive proof of the result by Martinsson [Ann. Appl. Prob. 26 (2016), Ann. Prob. 46 (2018)] concerning the leading order of the ground state.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47256335","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: 1

Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes 细胞大小有界的生长碎裂过程的强数定律

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-12-06 DOI: 10.30757/ALEA.v19-68

E. Horton, A. Watson

引用次数: 1

Two-sided immigration, emigration and symmetry properties of self-similar interval partition evolutions 自相似区间划分演化的双侧迁移、迁移和对称性

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-11-26 DOI: 10.30757/alea.v20-25

Quan Shi, Matthias Winkel

{"title":"Two-sided immigration, emigration and symmetry properties of self-similar interval partition evolutions","authors":"Quan Shi, Matthias Winkel","doi":"10.30757/alea.v20-25","DOIUrl":"https://doi.org/10.30757/alea.v20-25","url":null,"abstract":"Forman et al. (2020+) constructed $(alpha,theta)$-interval partition evolutions for $alphain(0,1)$ and $thetage 0$, in which the total sums of interval lengths (\"total mass\") evolve as squared Bessel processes of dimension $2theta$, where $thetage 0$ acts as an immigration parameter. These evolutions have pseudo-stationary distributions related to regenerative Poisson--Dirichlet interval partitions. In this paper we study symmetry properties of $(alpha,theta)$-interval partition evolutions. Furthermore, we introduce a three-parameter family ${rm SSIP}^{(alpha)}(theta_1,theta_2)$ of self-similar interval partition evolutions that have separate left and right immigration parameters $theta_1ge 0$ and $theta_2ge 0$. They also have squared Bessel total mass processes of dimension $2theta$, where $theta=theta_1+theta_2-alphage-alpha$ covers emigration as well as immigration. Under the constraint $max{theta_1,theta_2}gealpha$, we prove that an ${rm SSIP}^{(alpha)}(theta_1,theta_2)$-evolution is pseudo-stationary for a new distribution on interval partitions, whose ranked sequence of lengths has Poisson--Dirichlet distribution with parameters $alpha$ and $theta$, but we are unable to cover all parameters without developing a limit theory for composition-valued Markov chains, which we do in a sequel paper.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47694958","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: 3

Extinction probabilities in branching processes with countably many types: a general framework 具有可数多类型分支过程的灭绝概率:一般框架

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-11-19 DOI: 10.30757/alea.v19-12

D. Bertacchi, Peter Braunsteins, S. Hautphenne, F. Zucca

引用次数: 2

Fractionally Integrated Moving Average Stable Processes With Long-Range Dependence 具有长程依赖性的分数积分移动平均稳定过程

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-11-11 DOI: 10.30757/alea.v19-23

G. Feltes, S. Lopes

引用次数: 0