Related papers: Dimensionality-induced dynamical phase transition …

Dynamical phase transitions (DPTs) arise from qualitative changes in the long-time behavior of stochastic trajectories, often observed in systems with kinetic constraints or driven out of equilibrium. Here we demonstrate that first-order…

We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…

We study the dynamical phase transitions (DPTs) appearing for a single Brownian particle without drift. We first explore how first-order DPTs in large deviations can be found even for a single Brownian particle without any force upon…

We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution…

Let $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in $\rr$, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable L\'evy process $X=\{X_t, t \ge 0\}$ of…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

In [4], it is proved that we can have a continuous first-passage-time density function of one dimensional standard Brownian motion when the boundary is H\"older continuous with exponent greater than 1/2. For the purpose of extending [4]…

Let \{B_t^H,t\geq0\} be a d-dimensional fractional Brownian motion. We prove that the approximation of the first-order derivative of self-intersection local time, defined as…

We study the fluctuations of the area $A=\int_0^T x(t) dt$ under a one-dimensional Brownian motion $x(t)$ in a trapping potential $\sim |x|$, at long times $T\to\infty$. We find that typical fluctuations of $A$ follow a Gaussian…

In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the…

We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…

For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over…

We study a gas of $N$ Brownian particles in the presence of a common stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. Starting from all the particles localized at the origin, the…

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…

We study theoretically, experimentally and numerically the probability distribution $F(t_f|x_0,L)$ of the first passage times $t_f$ needed by a freely diffusing Brownian particle to reach a target at a distance $L$ from the initial position…

We study large fluctuations of the area $\mathcal{A}$ under a Brownian excursion $x(t)$ on the time interval $|t|\leq T$, constrained to stay away from a moving wall $x_0(t)$ such that $x_0(-T)=x_0(T)=0$ and $x_0(|t|<T)>0$. We focus on wall…

We study the local dynamical fluctuations in glass-forming models of particles embedded in $d$-dimensional space, in the mean-field limit of $d\to\infty$. Our analytical calculation reveals that single-particle observables, such as squared…

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…

We consider high frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of various classical statistics related to the local times of the…