Probability Theory and Related Fields最新文献

英文中文

On the ergodicity of interacting particle systems under number rigidity 数刚性下相互作用粒子系统的遍历性

IF 2 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-12-02 DOI: 10.1007/s00440-023-01243-3

Kohei Suzuki

In this paper, we provide relations among the following properties:

(a)
the tail triviality of a probability measure (mu ) on the configuration space ({varvec{Upsilon }});
(b)
the finiteness of a suitable (L^2)-transportation-type distance (bar{textsf {d} }_{varvec{Upsilon }});
(c)
the irreducibility of local ({mu })-symmetric Dirichlet forms on ({varvec{Upsilon }}).

As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including (text {sine}_{2}), (text {Airy}_{2}), (text {Bessel}_{alpha , 2}) ((alpha ge 1)), and (text {Ginibre}) point processes. In particular, the case of the unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role.

本文给出了以下性质之间的关系:(a)一个概率测度(mu )在位形空间({varvec{Upsilon }})上的尾平凡性;(b)一个合适的(L^2) -输运型距离(bar{textsf {d} }_{varvec{Upsilon }})的有限性;(c) ({varvec{Upsilon }})上局部({mu }) -对称Dirichlet形式的不可约性。作为一个应用，我们得到了具有对数相互作用的相互作用的无限扩散的遍历性(即收敛到平衡)，这些扩散产生于确定/永久的点过程，包括(text {sine}_{2}), (text {Airy}_{2}), (text {Bessel}_{alpha , 2}) ((alpha ge 1))和(text {Ginibre})点过程。特别地，未标记的戴森-布朗运动的情况被涵盖。对于证明，Ghosh-Peres意义上的点过程的数刚性起着关键作用。

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引用次数: 1

Retrospective Cohort Study on the Surgical Outcomes of Intracapsular Thyroidectomy Vs Standard Thyroidectomy. 甲状腺囊内切除术与标准甲状腺切除术手术效果的回顾性队列研究。

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-12-01 Epub Date: 2023-07-24 DOI: 10.1007/s12070-023-04074-9

S Meenakshi, M K Rajasekar, Sumitha Ramanathan

The focal point of thyroidectomy surgery has always been to reduce the incidence of inadvertent damage to the recurrent laryngeal nerve(RLN). The intracapsular thyroidectomy is one such technique with minimum chance of injuring the nerve. To compare retrospectively the surgical outcomes between the two methods of thyroidectomy-coventional thyroidectomy Vs intracapsular thyroidectomy. Materials and methods-55 cases of benign thyroid disease for whom thyroidectomy was performed in our hospital between the period of 2019-2022 were compared retrospectively. Out of these 34 cases had undergone intracapsular thyroidectomy and 21 cases underwent routine extracapsular thyroidectomy. The surgical outcomes including operation time, pain, postoperative infection, postoperative hypocalcemia, postoperative recurrent laryngeal nerve paralysis and mean hospital stay were analyzed. The mean operating time were very low in the intracapsular limb as compared to the other group. The pain and the mean hospital stay was also far lesser for the intracapsular limb. Both cohorts had no incidence of hypocalcemia. The incidence of recurrent laryngeal nerve palsy was very low in the intracapsular cohort (only 1 case of temporary unilateral RLN palsy), whereas it was higher in the routine extracapsular cohort (5 cases of permanent palsy). The risk of having vocal cord palsy (left/right) is 1.172 times more with conventional/standard thyroidectomy as compared to intracapsular thyroidectomy. Intracapsular technique is a much more rewarding method to perform thyroidectomy, without the risk of the recurrent laryngeal nerve palsy as compared to routine thyroidectomy.

甲状腺切除术的重点一直是减少喉返神经(RLN)意外损伤的发生率。囊内甲状腺切除术是一种损伤神经的可能性最小的技术。回顾性比较常规甲状腺切除术与囊内甲状腺切除术两种手术方式的手术效果。材料与方法:对2019-2022年我院行甲状腺切除术的55例良性甲状腺疾病患者进行回顾性比较。其中34例行甲状腺囊内切除术，21例行常规甲状腺囊外切除术。分析手术结果，包括手术时间、疼痛、术后感染、术后低钙、术后喉返神经麻痹和平均住院时间。与其他组相比，囊内肢体的平均手术时间很短。囊内肢体的疼痛和平均住院时间也要少得多。两个队列均未发生低钙血症。喉返神经麻痹在囊内组的发生率很低(只有1例暂时性单侧RLN麻痹)，而在常规囊外组的发生率较高(5例永久性麻痹)。与囊内甲状腺切除术相比，常规/标准甲状腺切除术发生声带麻痹(左/右)的风险是1.172倍。与常规甲状腺切除术相比，囊内技术是一种更有益的甲状腺切除术方法，没有喉返神经麻痹的风险。

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引用次数: 0

Half-space depth of log-concave probability measures 对数凹概率测度的半空间深度

IF 2 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-11-29 DOI: 10.1007/s00440-023-01236-2

Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis

Given a probability measure (mu ) on ({{mathbb {R}}}^n), Tukey’s half-space depth is defined for any (xin {{mathbb {R}}}^n) by (varphi _{mu }(x)=inf {mu (H):Hin {{{mathcal {H}}}}(x)}), where (mathcal{H}(x)) is the set of all half-spaces H of ({{mathbb {R}}}^n) containing x. We show that if (mu ) is a non-degenerate log-concave probability measure on ({{mathbb {R}}}^n) then

$$begin{aligned} e^{-c_1n}leqslant int _{{mathbb {R}}^n}varphi _{mu }(x),dmu (x) leqslant e^{-c_2n/L_{mu }^2} end{aligned}$$

where (L_{mu }) is the isotropic constant of (mu ) and (c_1,c_2>0) are absolute constants. The proofs combine large deviations techniques with a number of facts from the theory of (L_q)-centroid bodies of log-concave probability measures. The same ideas lead to general estimates for the expected measure of random polytopes whose vertices have a log-concave distribution.

给定一个概率测度 (mu ) on ({{mathbb {R}}}^n)， Tukey的半空间深度定义为任何 (xin {{mathbb {R}}}^n) 通过 (varphi _{mu }(x)=inf {mu (H):Hin {{{mathcal {H}}}}(x)})，其中 (mathcal{H}(x)) 所有半空间的集合H是什么 ({{mathbb {R}}}^n) 包含x，我们证明了 (mu ) 一个非退化对数凹概率测度在 ({{mathbb {R}}}^n) 然后 $$begin{aligned} e^{-c_1n}leqslant int _{{mathbb {R}}^n}varphi _{mu }(x),dmu (x) leqslant e^{-c_2n/L_{mu }^2} end{aligned}$$在哪里 (L_{mu }) 各向同性常数是 (mu ) 和 (c_1,c_2>0) 都是绝对常数。这些证明结合了大偏差技术和来自理论的大量事实 (L_q)-对数凹概率测度的质心体。同样的思想导致了对顶点为对数凹分布的随机多面体的期望测度的一般估计。

引用次数: 4

Edge statistics for lozenge tilings of polygons, I: concentration of height function on strip domains 多边形菱形平铺的边缘统计，I:高度函数在条形域上的集中

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-11-14 DOI: 10.1007/s00440-023-01238-0

Jiaoyang Huang

引用次数: 0

Harnack inequality and one-endedness of UST on reversible random graphs 可逆随机图上的哈纳克不等式和UST的一端性

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-11-08 DOI: 10.1007/s00440-023-01239-z

Nathanaël Berestycki, Diederik van Engelenburg

Abstract We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al. (Ann Probab 29(1):1–65, 2001). Furthermore, we make progress towards a conjecture of Aldous and Lyons by proving that these conditions are fulfilled for strictly subdiffusive recurrent unimodular graphs. Finally, we discuss the behaviour of the random walk conditioned to never return to the origin, which is well defined as a consequence of our results.

摘要证明了对于循环可逆图，下列条件是等价的:(a)势核的存在唯一性，(b)从无穷远处调和测度的存在唯一性，(c)一个新的锚定的Harnack不等式，(d)有线一致生成树的单端性。特别地，这给出了在upt上锚定的(实际上也是椭圆的)哈纳克不等式的证明。这也补充和加强了Benjamini等人(Ann Probab 29(1):1 - 65,2001)的一些结果。进一步证明了严格次扩散递归非模图满足这些条件，从而进一步证明了Aldous和Lyons的一个猜想。最后，我们讨论了随机漫步的行为，这种行为被限制为永远不会返回原点，这是我们的结果的结果。

引用次数: 2

Optimal transport methods for combinatorial optimization over two random point sets 两个随机点集组合优化的最优传输方法

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-11-07 DOI: 10.1007/s00440-023-01245-1

Michael Goldman, Dario Trevisan

Abstract We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $$mathbb {R}^d$$ R d where the edge cost between two points is given by a p th power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and $$d ge 3, 1le p d ≥ 3 , 1 ≤ p < d . Previous results were limited to the range $$p p < d / 2 . Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques.

研究了在$$mathbb {R}^d$$ R d中随机二部几何图上的一类组合优化问题的最小代价，其中两点之间的边代价由它们的欧几里得距离的p次幂给出。这包括旅行销售问题和有界度最小生成树。当点均匀分布且$$d ge 3, 1le p<d$$ d≥3,1≤p ＆lt;D。先前的结果仅限于$$p<d/2$$ p ＆lt;D / 2。我们的证明基于子可加性方法，并建立在欧几里得二部匹配问题随机实例的新边界上，通过其最优传输松弛和泛函分析技术获得。

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引用次数: 2

On the lack of Gaussian tail for rough line integrals along fractional Brownian paths 分数阶布朗路径粗糙线积分的高斯尾缺失问题

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-10-30 DOI: 10.1007/s00440-023-01242-4

H. Boedihardjo, X. Geng

Abstract We show that the tail probability of the rough line integral $$int _{0}^{1}phi (X_{t})dY_{t}$$ ∫ 0 1 ϕ ( X t ) d Y t , where ( X , Y ) is a 2D fractional Brownian motion with Hurst parameter $$Hin (1/4,1/2)$$ H ∈ ( 1 / 4 , 1 / 2 ) and $$phi $$ ϕ is a $$C_{b}^{infty }$$ C b ∞ -function satisfying a mild non-degeneracy condition on its derivative, cannot decay faster than a $$gamma $$ γ -Weibull tail with any exponent $$gamma >2H+1$$ γ > 2 H + 1 . In particular, this produces a simple class of examples of differential equations driven by fBM, whose solutions fail to have Gaussian tail even though the underlying vector fields are assumed to be of class $$C_{b}^{infty }$$ C b ∞ . This also demonstrates that the well-known upper tail estimate proved by Cass–Litterer–Lyons in 2013 is essentially sharp.

摘要我们证明了粗线积分$$int _{0}^{1}phi (X_{t})dY_{t}$$∫0 1 φ (X t) d Y t的尾部概率，其中(X, Y)是一个具有Hurst参数$$Hin (1/4,1/2)$$ H∈(1 / 4,1 / 2)的二维分数阶布朗运动，$$phi $$ φ是一个满足其导数的温和非简并条件的$$C_{b}^{infty }$$ C b∞函数，不能比具有任意指数$$gamma >2H+1$$ γ ＆gt的$$gamma $$ γ -威布尔尾部衰减得更快;2h + 1。特别是，这产生了一类由fBM驱动的微分方程的简单例子，即使假设底层向量场为$$C_{b}^{infty }$$ C b∞类，其解也不具有高斯尾。这也证明了由Cass-Litterer-Lyons在2013年证明的众所周知的上尾估计本质上是尖锐的。

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引用次数: 1

Quantitative stability of barycenters in the Wasserstein space Wasserstein空间中质心的定量稳定性

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-10-25 DOI: 10.1007/s00440-023-01241-5

Guillaume Carlier, Alex Delalande, Quentin Merigot

Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures of interest are often not accessible in their entirety and the practitioner may have to deal with statistical or computational approximations instead. In this article, we quantify the effect of such approximations on the corresponding barycenters. We show that Wasserstein barycenters depend in a Hölder-continuous way on their marginals under relatively mild assumptions. Our proof relies on recent estimates that allow to quantify the strong convexity of the barycenter functional. Consequences regarding the statistical estimation of Wasserstein barycenters and the convergence of regularized Wasserstein barycenters towards their non-regularized counterparts are explored.

瓦瑟斯坦质心以一种几何上有意义的方式定义了概率测度的平均值。它们在图像、几何或语言处理等应用领域的应用越来越普遍。然而，在这些领域中，感兴趣的概率度量通常不能完整地访问，从业者可能不得不处理统计或计算近似。在本文中，我们量化了这种近似对相应质心的影响。我们表明，在相对温和的假设下，Wasserstein质心以Hölder-continuous的方式依赖于它们的边际。我们的证明依赖于最近的估计，这些估计允许量化重心泛函的强凸性。探讨了Wasserstein质心的统计估计和正则化Wasserstein质心向非正则化质心收敛的结果。

引用次数: 0

Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters 非相容图上的微超临界渗流II:无限团簇的生长和等渗

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-10-17 DOI: 10.1007/s00440-023-01240-6

Tom Hutchcroft

引用次数: 1

On the pitchfork bifurcation for the Chafee–Infante equation with additive noise 加性噪声下Chafee-Infante方程的干草叉分岔

1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields

Pub Date : 2023-10-05 DOI: 10.1007/s00440-023-01235-3

Alex Blumenthal, Maximilian Engel, Alexandra Neamtu

引用次数: 9

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