Probability distributions for the run-and-tumble models with variable speed and tumbling rate

run-and-tumble粒子的稳态涨落

Stationary fluctuations of run-and-tumble particles

该文研究独立及带排斥相互作用的run-and-tumble粒子的稳态涨落，证明粒子联合密度收敛于无限维Ornstein-Uhlenbeck过程，得到总密度非马尔可夫高斯过程的协方差闭式解，并通过小噪声极限得到含记忆项的大偏差速率函数。

活动驱动聚类与刚性粒子的多体稳态

Activity-driven clustering and many-body steady state of jamming run-and-tumble particles

该研究通过微观动态解析了刚性粒子的多体稳态结构，揭示了活动参数对集群组织和稳态行为的调控作用。

Central limit theorem and large deviations for run and tumble particles on a lattice

We study run and tumble particles on the one-dimensional lattice $\mathbb{Z}$. We explicitly compute the Fourier-Laplace transform of the position of the particle and as a consequence obtain explicit expressions for the diffusion constant and the large deviation free energy function. We also do the same computations in a corresponding continuum model. In the latter, when adding an external field, we can explicitly compute the large deviation free energy, and the deviation from the Einstein relation due to activity. Finally, we generalize the model to the $d$-dimensional lattice $\mathbb{Z}^d$,…

一维奔跑翻滚粒子的吸收边界条件与硬墙边界条件之间的关联

Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle

本文研究一维奔跑翻滚粒子在任意外力下吸收边界与硬墙边界的对偶性，建立逸出概率与硬墙位置累积分布的关系，并通过稳态显式计算、Fokker-Planck 推导及数值模拟验证。

关于细菌趋化性的 run and tumble 方程的渐近行为

On the asymptotic behaviour of a run and tumble equation for bacterial chemotaxis

本文研究细菌趋化性 run and tumble 方程的渐近行为，利用 Harris 定理证明了线性及弱非线性方程在任意维度下以指数速率收敛到唯一稳态解，并构造了弱非线性模型的稳态解及亚强制性结果。

Survival probability of a run-and-tumble particle in the presence of a drift

We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate $γ$, the (new) velocity of the particle is drawn randomly from a distribution $W(v)$. We study the survival probability $S(x,t)$ of a particle starting from $x \geq 0$ up to time $t$ and obtain an explicit expression for its double Laplace transform (with respect to both $x$ and $t$) for an arbitrary velocity distribution $W(v)$, not necessarily symmetric. This result is obtained as a consequ…

Run-and-tumble motion: the role of reversibility

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the `active part' of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and fre…

反常随机飞行与时间分数阶跑动-翻滚方程

Anomalous random flights and time-fractional run-and-tumble equations

本文将d维随机飞行的一般性分析扩展至由动力学方程非局部广义化产生的时间分数阶过程，通过时间分数阶方程解的概率解释导出原始输运过程的时间变换版本，并重点研究了一维电报过程的时间分数阶方程及其随机解。