Markov Processes and Related Fields最新文献

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Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media 极限周期介质中的均匀安德森定位和非局部迷你型估算

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2024-01-02 DOI: 10.61102/1024-2953-mprf.2023.29.4.004

V. Chulaevsky, Y. Suhov

We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit-periodic lattice Schr¨odinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new corre- lation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.

我们证明了一类极限周期晶格施罗丁格算子的特征函数均匀指数定位和谱的简单性。证明的一个重要成分是著名的南估计（特征值的相关不等式）的广义变体，它适用于谱区间可以任意置于实线上的情况。新的相关不等式使我们能够大幅简化 KAM（Kolmogorov-Arnold-Moser）技术的应用，并使其更加透明。

引用次数: 0

Persistence in Perturbed Contact Models in Continuum 连续介质中受扰动接触模型的持久性

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2024-01-02 DOI: 10.61102/1024-2953-mprf.2023.29.4.003

P. Sergey, Z. Elena

Can a local disaster lead to extinction? We answer this question in this work. In the paper [19] we considered contact processes on locally compact metric spaces with state dependent birth and death rates and formulated suf- ﬁcient conditions on the rates that ensure the existence of invariant measures. One of the crucial conditions in [19] was the critical regime condition, which meant the existence of a balance between birth and death rates in average. In the present work, we reject the criticality condition and suppose that the bal- ance condition is violated. This implies that the evolution of the correlation functions of the contact model under consideration is determined by a nonlocal convolution type operator perturbed by a (negative) potential. We show that local peaks in mortality do not typically lead to extinction. We prove that a family of invariant measures exists even without the criticality condition and these measures can be described using the Feynman-Kac formula.

局部灾害会导致物种灭绝吗？我们在本文中回答了这个问题。在论文[19]中，我们考虑了局部紧凑度量空间上与状态相关的出生率和死亡率的接触过程，并对确保存在不变度量的出生率和死亡率提出了有利条件。[19]中的一个关键条件是临界制度条件，即平均出生率和死亡率之间存在平衡。在本研究中，我们摒弃了临界条件，假设违反了平衡条件。这意味着所考虑的接触模型的相关函数的演变是由一个受（负）电势扰动的非局部卷积型算子决定的。我们证明，死亡率的局部峰值通常不会导致物种灭绝。我们证明，即使不存在临界条件，也存在一系列不变度量，这些度量可以用费曼-卡克公式来描述。

引用次数: 0

Diﬀusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates 具有多项式速率的对称生死过程的融合近似法

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2024-01-02 DOI: 10.61102/1024-2953-mprf.2023.29.4.007

A. Logachov, O. Logachova, E. Pechersky, E. Presman, A. Yambartsev

The symmetric birth and death stochastic process on the non-negative integers x ∈ Z + with polynomial rates x α , α ∈ [1, 2], x 6= 0, is studied. The process moves slowly and spends more time in the neighborhood of the state 0. We prove the convergence of the scaled process to a solution of stochastic diﬀerential equation without drift. Sticking phenomenon appears at the limiting process: trajectories, starting from any state, take ﬁnite time to reach 0 and remain there indeﬁnitely.

本文研究了在非负整数 x∈Z + 上以多项式速率 x α , α∈ [1, 2], x 6= 0 的对称出生和死亡随机过程。该过程移动缓慢，在状态 0 附近停留的时间较长。我们证明了缩放过程对无漂移随机二阶方程解的收敛性。在极限过程中会出现粘滞现象：从任何状态出发的轨迹都需要花费有限的时间到达 0，并无限地停留在那里。

引用次数: 0

Minimal Action Principle for Gravity and Electrodynamics, Einstein Lambda, and Lagrange Points 引力和电动力学的最小作用原理、爱因斯坦蓝姆达和拉格朗日点

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2024-01-02 DOI: 10.61102/1024-2953-mprf.2023.29.4.005

V.V. Vedenyapin, A.A. Bay, V. I. Parenkina, A.G. Petrov

The relativistic equations of gravitation and electromagnetism in the form of Vlasov – Einstein – Maxwell equations are proposed and analyzed. For weakly relativistic equations we get an analog of Mealn – McCree solution. We also study Lagrange points in non-relativistic case with Einstein lambda- term.

提出并分析了弗拉索夫-爱因斯坦-麦克斯韦方程形式的引力和电磁相对论方程。对于弱相对论方程，我们得到了类似于 Mealn - McCree 的解。我们还研究了带有爱因斯坦λ项的非相对论情况下的拉格朗日点。

引用次数: 0

Wick–Fourier–Hermite Series in the Theory of Linear and Nonlinear Transformations of Gaussian Distributions 高斯分布线性和非线性变换理论中的 Wick-Fourier-Hermite 系列

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2024-01-02 DOI: 10.61102/1024-2953-mprf.2023.29.4.001

E. Chernousova, S. Molchanov, A. Shiryaev

This article provides information on Hermite polynomials and its application to some problems in risk theory and site percolation.

本文介绍赫米特多项式及其在风险理论和站点渗流中的应用。

引用次数: 0

On Malyshev’s Method of Automorphic Functions in Diﬀraction by Wedges 论马利雪夫的楔衍射自动函数法

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2023-12-22 DOI: 10.61102/1024-2953-mprf.2023.29.4.002

A. Komech, A. Merzon

We describe Malyshev’s method of automorphic functions in ap- plication to boundary value problems in angles and to diﬀraction by wedges. We give a concise survey of related results of A. Sommerfeld, S.L. Sobolev, J.B. Keller, G.E. Shilov and others.

我们描述了马利舍夫的自动函数方法在角的边界值问题和楔的二分法中的应用。我们对索默费尔德（A. Sommerfeld）、索博列夫（S.L. Sobolev）、凯勒（J.B. Keller）、希洛夫（G.E. Shilov）等人的相关研究成果进行了简要介绍。

引用次数: 0

Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media 周期介质中卷积型非自治算子的均匀化

4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2023-10-16 DOI: 10.61102/1024-2953-mprf.2023.29.2.001

A. Piatnitski, E. Zhizhina

The paper deals with periodic homogenization problem for a para- bolic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scal- ing is diffusive, that is, the scaling factor of the temporal variable is equal to the square of the scaling factor of the spatial variable. Under the assumption that the convolution kernel has a nite second moment and that the operator is symmetric in spatial variables we show that the equation under study ad- mits homogenization, and we prove that the limit operator is a second order differential parabolic operator with constant coefficients.

研究一类椭圆部分为快速振荡系数的卷积型算子的准曲型方程的周期均匀化问题。假设系数在空间变量和时间变量中都是快速振荡的周期函数，并且尺度是扩散的，即时间变量的尺度因子等于空间变量的尺度因子的平方。在卷积核有二阶矩和算子在空间变量上对称的假设下，证明了所研究的方程可以齐次化，并证明了极限算子是常系数二阶微分抛物算子。

引用次数: 1

Random walk on the Poincaré disk induced by a group of Möbius transformations. 由一组Möbius变换引起的庞卡罗圆盘上的随机漫步。

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2019-01-01

Charles McCarthy, Gavin Nop, Reza Rastegar, Alexander Roitershtein

We consider a discrete-time random motion, Markov chain on the Poincaré disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random Möbius transformations. We exploit an isomorphism between the underlying group of Möbius transformations and $ℝ$ to study the random motion through its relation to a one-dimensional random walk. More specifically, we show that key geometric characteristics of the random motion, such as Busemann functions and bipolar coordinates evaluated at its location, and hyperbolic distance from the origin, can be either explicitly computed or approximated in terms of the random walk. We also consider a variant of the model where the motion is not confined to a single arc, but rather the particle switches between arcs of a parabolic pencil of circles at random times.

我们考虑一个离散时间随机运动，庞卡卡尔圆盘上的马尔可夫链。在该模型的基本变体中，粒子沿着圆盘内的某些圆弧运动，其位置由随机Möbius变换的组合决定。我们利用底层的Möbius变换群与l之间的同构关系，通过它与一维随机游走的关系来研究随机运动。更具体地说，我们表明随机运动的关键几何特征，如Busemann函数和在其位置评估的双极坐标，以及到原点的双曲线距离，可以通过随机行走显式计算或近似。我们还考虑了模型的一种变体，其中运动不局限于单个弧，而是粒子在随机时间在抛物线形圆铅笔的弧之间切换。

引用次数: 0

Absorption Time and Tree Length of the Kingman Coalescent and the Gumbel Distribution 金曼花的吸收时间、树长与甘贝尔分布

IF 0.2 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields

Pub Date : 2015-01-01 DOI: 10.15496/PUBLIKATION-9137

M. Möhle

Formulas are provided for the cumulants and the moments of the time T back to the most recent common ancestor of the Kingman coalescent. It is shown that both the jth cumulant and the jth moment of T are linear combinations of the values ζ(2m), m ∈ {0, . . . , bj/2c}, of the Riemann zeta function ζ with integer coefficients. The proof is based on a solution of a two-dimensional recursion with countably many initial values. A closely related strong convergence result for the tree length Ln of the Kingman coalescent restricted to a sample of size n is derived. The results give reason to revisit the moments and central moments of the classical Gumbel distribution.

公式提供了累积量和时间的时刻T回到最近的共同祖先的金曼聚结。证明了T的第j个累积量和第j个矩是下列值的线性组合:ζ(2m)， m∈{0，…， bj/2c}，具有整数系数的黎曼ζ函数。该证明是基于一个具有可数多个初值的二维递归的解。在样本大小为n的情况下，导出了Kingman聚结的树长Ln的一个密切相关的强收敛结果。这些结果使我们有理由重新审视经典冈贝尔分布的矩和中心矩。

引用次数: 1

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