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Hanshuang Chen

Publications and source records attributed to Hanshuang Chen.

At least 19 recordsLinked to original sources
arXiv2025

Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion

We study the fluctuation properties of the local time density, ${ρ_T} = \frac{1}{T}\int_0^T {δ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial distance from the particle to the origin. In the large observation time limit, $T \to \infty$, the local time density $ρ_T$ obeys the large deviation principle, $P(ρ_T= ρ) \sim e^{-T I(ρ)}$, where the rate function $I(ρ)$ is analytic everywhere for $d\leq 4$. In contrast, for $d>4$, $I(ρ)$ becomes nonanalytic at a specific point $ρ=ρ_c^{(d)}$, where $ρ_c^{(d)}=d(d-4)/(2d-4)$ depends solely on dimensionality. The singularity signals the occurrence of a first-order dynamical phase transition in dimensions higher than four. Such a transition is accompanied by temporal phase separations in the large deviations of Brownian trajectories. Finally, we validate our theoretical results using a rare-event simulation approach.

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arXiv2025

Pairwise correlations of global times in one-dimensional Brownian motion under stochastic resetting

Brownian motion with stochastic resetting-a process combining standard diffusion with random returns to a fixed position-has emerged as a powerful framework with applications spanning statistical physics, chemical kinetics, biology, and finance. In this study, we investigate the mutual correlations among three global characteristic times for one-dimensional resetting Brownian motion $x(τ)$ over the interval $τ\in \left[ 0, t\right] $: the occupation time $t_o$ spent on the positive semi-axis, the time $t_m$ at which $x(τ)$ attains its global maximum, and the last-passage time $t_{\ell}$ when the process crosses the origin. For the process starting from the origin and undergoing Poissonian resetting back to the origin, we analytically compute the pairwise joint distributions of these three times (in the Laplace domain) and derive their pairwise correlation coefficients. Our results reveal that these global times display rich correlations, with a non-trivial dependence on the resetting rate $r$. Specifically, we find that (i) While $t_{o}$ and $t_{\ell}^m$ are uncorrelated for any positive integer $m$, $t_{o}^2$ and $t_{\ell}^m$ display anti-correlation; (ii) A positive correlation exists between $t_{o}$ and $t_{m}$, which decays toward zero following a logarithmically corrected power-law way with an exponent of $-2$ as $r \to \infty$; (iii) The correlation between $t_{m}$ and $t_{\ell}$ shifts from positive to negative as $r$ increases. All analytical predictions are validated by extensive numerical simulations.

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arXiv2025

First-passage and extreme value statistics for overdamped Brownian motion in a linear potential

We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=μ|x-x_0|$, where $μ>0$ is the strength of the potential and $x_0>0$ is the position of the lowest point of the potential, which coincides with the starting position of the particle. The Brownian motion terminates whenever the particle passes through the origin at a random time $t_f$. Our study reveals that the mean first-passage time $\langle t_f \rangle$ exhibits a nonmonotonic behavior with respect to $μ$, with a unique minimum occurring at an optimal value of $μ\simeq 1.24468D/x_0$, where $D$ is the diffusion constant of the Brownian particle. Moreover, we examine the distribution $P(M|x_0)$ of the maximum displacement $M$ during the first-passage process, as well as the statistics of the time $t_m$ at which $M$ is reached. Intriguingly, there exists another optimal $μ\simeq 1.24011 D/x_0$ that minimizes the mean time $\langle t_m \rangle$. All our analytical findings are corroborated through numerical simulations.

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arXiv2024

Short-time large deviations of first-passage functionals for high-order stochastic processes

We consider high-order stochastic processes $x(t)$ described by the Langevin equation $\frac{{{d^m}x\left( t \right)}}{d{t^m}}= \sqrt{2D} ξ(t)$, where $ξ(t)$ is a delta-correlated Gaussian noise with zero mean, and $D$ is the strength of noise. We focus on the short-time statistics of the first-passage functionals $A=\int_{0}^{T} \left[ x(t)\right] ^n dt$ along the trajectories starting from $x(0)=L$ and terminating whenever passing through the origin for the first-time at $t=T$. Using the optimal fluctuation method, we analytically obtain the most likely realizations of the first-passage processes for a given constraint $A$ with $n=0$ and 1, corresponding to the first-passage time itself and the area swept by the first-passage trajectory, respectively. The tail of the distribution of $A$ shows an essential singularity at $A \to 0$, $P_{m,n}(A |L) \sim \exp\left(-\frac{α_{m,n}L^{2mn-n+2}}{D A^{2m-1}} \right)$, where the explicit expressions for the exponents $α_{m,0}$ and $α_{m,1}$ for arbitrary $m$ are obtained.

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arXiv2024

Short-time large deviation of constrained random acceleration process

By optimal fluctuation method, we study short-time distribution $P(\mathcal{A}=A)$ of the functionals, $\mathcal{A}=\int_{0}^{t_f} x^n(t) dt$, along constrained trajectories of random acceleration process for a given time duration $t_f$, where $n$ is a positive integer. We consider two types of constraints: one is called the total constraint, where the initial position and velocity and the final position and velocity are both fixed, and the other is called the partial constraint, where the initial position and velocity, the final position are fixed, and letting the final velocity be free. Via the variation of constrained action functionals, the resulting Euler-Lagrange equations are analytically solved for $n=1$ and 2, and the optimal path, i.e., the most probable realization of the random acceleration process $x(t)$, conditioned on specified $A$ and $n$, are correspondingly obtained. For $n \geq 3$, a numerical scheme is proposed to find the optimal path. We show that, for $n=1$, $P(A)$ is a Gaussian distribution with the variance proportional to $Dt_f^5$ ($D$ is the particle velocity diffusion constant). For $n \geq 2$, $P(A)$ exhibits the non-Gaussian feature. In the small-$A$ limit, $P(A)$ show a essential singularity, $-\ln P(A) \sim A^{-3}$, and the optimal path localizes around the initial state over a long-time window, and then escapes to the final position sharply at a late time. For $A$ much larger than its typical value, there are multiple optimal paths with the same $A$ but with different actions (or probability densities). Among these degenerate paths, one with the minimum action is dominant, and the others are exponentially unlikely. All the theoretical results are validated by simulating the effective Langevin equations governing the constrained random acceleration process.

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arXiv2023

Extremal statistics for a one-dimensional Brownian motion with a reflective boundary

We investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant $D$) during a time interval $\left[0, t \right]$ in the presence of a reflective boundary at the origin, starting from a positive position $x_0$. By deriving the survival probability of the Brownian particle without hitting an absorbing boundary at $x=M$, we obtain the distribution $P(M|x_0,t)$ of the maximum displacement $M$ and its expectation $\langle M \rangle$. In the short-time limit, i.e., $t \ll t_d$ where $t_d=x_0^2/D$ is the diffusion time from the starting position $x_0$ to the reflective boundary at the origin, the particle behaves like a free Brownian motion without any boundaries. In the long-time limit, $t \gg t_d$, $\langle M \rangle$ grows with $t$ as $\langle M \rangle \sim \sqrt{t}$, which is similar to the free Brownian motion, but the prefactor is $π/2$ times of the free Brownian motion, embodying the effect of the reflective boundary. By solving the propagator and using a path decomposition technique, we obtain the joint distribution $P(M,t_m|x_0,t)$ of $M$ and the time $t_m$ at which this maximum is achieved, from which the marginal distribution $P(t_m|x_0,t)$ is also obtained. For $t \ll t_d$, $P(t_m|x_0,t)$ looks like a U-shaped attributed to the arcsine law of free Brownian motion. For $t$ equal to or larger than order of magnitude of $t_m$, $P(t_m|x_0,t)$ deviates from the U-shaped distribution and becomes asymmetric with respect to $t/2$. Moreover, we compute the expectation $\langle t_m \rangle$ of $t_m$, and find that $\langle t_m \rangle/t$ is an increasing function of $t$. In two limiting cases, $\langle t_m \rangle/t \to 1/2$ for $t \ll t_d$ and $\langle t_m \rangle/t \to (1+2G)/4 \approx 0.708$ for $t \gg t_d$, where $G\approx0.916$ is the Catalan's constant. All the theoretical results are validated by numerical simulations.

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arXiv2023

Epidemic extinction in a simplicial susceptible-infected-susceptible model

We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ($S+I \to 2I$) with a rate $β$ or by three-body interactions ($S+2I \to 3I$) with a rate $β(1+δ)$, and each infected individual spontaneously recovers ($I \to S$) with a rate $μ$. We focus on the case $δ>0$ that embodies a synergistic reinforcement effect in the group interactions. By using the theory of large fluctuations to solve approximately for the master equation, we reveal two different scenarios for optimal path to extinction, and derive the associated action $\mathcal{S}$ for $β_b<β<β_c$ and for $β>β_c$, where $β_b=4 (1+δ)/(2+δ)^2$ and $β_c=1$ are two different bifurcation points. The action $\mathcal{S}$ shows different scaling laws with the distance of the infectious rate to the transition points $β_b$ and $β_c$, characterized by two different exponents: 3/2 and 1, respectively. Interestingly, the second-order derivative of $\mathcal{S}$ with respect to $β$ is discontinuous at $β=β_c$, while $\mathcal{S}$ and its first-order derivative are both continuous, reminiscent of the second-order phase transitions in equilibrium systems. Finally, a rare-event simulation method is used to compute the mean extinction time, which depends exponentially on $\mathcal{S}$ and the size $N$ of the population. The simulations results are in well agreement with the proposed theory.

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arXiv2023

Extremal statistics for a resetting Brownian motion before its first-passage time

We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position $x_0$ ($>0$). By deriving the exit probability of RBM in an interval $\left[0, M \right] $ from the origin, we obtain the distribution $P_r(M|x_0)$ of the maximum displacement $M$ and thus gives the expected value $\langle M \rangle$ of $M$ as functions of the resetting rate $r$ and $x_0$. We find that $\langle M \rangle$ decreases monotonically as $r$ increases, and tends to $2 x_0$ as $r \to \infty$. In the opposite limit, $\langle M \rangle$ diverges logarithmically as $r \to 0$. Moreover, we derive the propagator of RBM in the Laplace domain in the presence of both absorbing ends, and then leads to the joint distribution $P_r(M,t_m|x_0)$ of $M$ and the time $t_m$ at which this maximum is achieved in the Lapalce domain by using a path decomposition technique, from which the expected value $\langle t_m \rangle$ of $t_m$ is obtained explicitly. Interestingly, $\langle t_m \rangle$ shows a nonmonotonic dependence on $r$, and attains its minimum at an optimal $r^{*} \approx 2.71691 D/x_0^2$, where $D$ is the diffusion coefficient. Finally, we perform extensive simulations to validate our theoretical results.

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arXiv2022

Non-equilibrium random walks on multiplex networks

We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to one of its replicas in another layer. We derive the so-called supra-Markov matrix that governs the evolution of the occupation probability of the walker. The occupation probability at stationarity is different from the weighted average over the counterparts on each layer, unless the transition probabilities between layers vanish. However, they are approximately equal when the transition probabilities between layers are very small, which is given by the first-order degenerate perturbation theory. Moreover, we compute the mean first passage time (MFPT) and the graph MFPT (GrMFPT) that is the average of the MFPT over all pairs of distinct nodes. Interestingly, we find that the GrMFPT can be smaller than that of any layer taken in isolation. The result embodies the advantage of global search on multiplex networks.

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arXiv2022

Random walks on complex networks under time-dependent stochastic resetting

We study discrete-time random walks on networks subject to a time-dependent stochastic resetting, where the walker either hops randomly between neighboring nodes with a probability $1-ϕ(a)$, or is reset to a given node with a complementary probability $ϕ(a)$. The resetting probability $ϕ(a)$ depends on the time $a$ since the last reset event (also called $a$ the age of the walker). Using the renewal approach and spectral decomposition of transition matrix, we formulize the stationary occupation probability of the walker at each node and the mean first passage time between arbitrary two nodes. Concretely, we consider that two different time-dependent resetting protocols that are both exactly solvable. One is that $ϕ(a)$ is a step-shaped function of $a$ and the other one is that $ϕ(a)$ is a rational function of $a$. We demonstrate the theoretical results on two different networks, also validated by numerical simulations, and find that the time-modulated resetting protocols can be more advantageous than the constant-probability resetting in accelerating the completion of a target search process.

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arXiv2022

Entropy rate of random walks on complex networks under stochastic resetting

Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to address how the entropy rate is affected by stochastic resetting in discrete-time Markovian processes, and explore nontrivial effects of the resetting in the mixing properties of a stochastic process. In particular, we consider resetting random walks on complex networks and compute the entropy rate as a function of the resetting probability. Interestingly, we find that the entropy rate can show a nonmonotonic dependence on the resetting probability. There exists an optimal resetting probability for which the entropy rate reaches a maximum. We also show that the maximum entropy rate can be larger than that of the maximal-entropy random walks on the same topology. Our study provides a new nontrivial effect of stochastic resetting on nonequilibrium statistical physics.

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arXiv2022

Random walks on complex networks under node-dependent stochastic resetting

In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation probabilities of the walker on each node and the mean first passage time between arbitrary two nodes. Finally, we demonstrate our theoretical results on three networks with two different resetting protocols, validated by numerical simulations as well. We find that under a delicate setting it is advantageous to optimize the efficiency of a global search on such networks by the node-dependent resetting probability.

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arXiv2022

First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry

We investigate the first passage properties of a Brownian particle diffusing freely inside a $d$-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate $γ$ and initial distance $r$ of the particle to the center of the sphere. We find that when $r>r_c$ there exists a nonzero optimal resetting rate $γ_{\rm opt}$ at which the MTA is a minimum, where $r_c=\sqrt {d/\left( {d + 4} \right)} R$ and $R$ is the radius of sphere. As $r$ increases, $γ_{\rm opt}$ exhibits a continuous transition from zero to nonzero at $r=r_c$. Furthermore, we consider that the particle lies in between two two-dimensional or three-dimensional concentric spheres, and obtain the domain in which resetting expedites the MTA, which is $(R_1, r_{c_1}) \cup (r_{c_2},R_2)$, with $R_1$ and $R_2$ being the radius of inner and outer spheres, respectively. Interestingly, when $R_1/R_2$ is less than a critical value, $γ_{\rm opt}$ exhibits a discontinuous transition at $r=r_{c_1}$; otherwise, such a transition is continuous. However, at $r=r_{c_2}$, $γ_{\rm opt}$ always shows a continuous transition.

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arXiv2021

First passage in discrete-time absorbing Markov chains under stochastic resetting

First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this paper, we study the effect of stochastic resetting on first passage properties of discrete-time absorbing Markov chains, described by a transition matrix $\brm{Q}$ between transient states and a transition matrix $\brm{R}$ from transient states to absorbing states. Using a renewal approach, we exactly derive the unconditional mean first passage time (MFPT) to either of absorbing states, the splitting probability the and conditional MFPT to each absorbing state. All the quantities can be expressed in terms of a deformed fundamental matrix $\brm{Z_γ}=\left[\brm{I}-(1-γ) \brm{Q} \right]^{-1}$ and $\brm{R}$, where $\brm{I}$ is the identity matrix, and $γ$ is the resetting probability at each time step. We further show a sufficient condition under which the unconditional MPFT can be optimized by stochastic resetting. Finally, we apply our results to two concrete examples: symmetric random walks on one-dimensional lattices with absorbing boundaries and voter model on complete graphs.

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arXiv2021

Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks

By constructing a multicanonical Monte Carlo simulation, we obtain the full probability distribution $ρ_N(r)$ of the degree assortativity coefficient $r$ on configuration networks of size $N$ by using the multiple histogram reweighting method. We suggest that $ρ_N(r)$ obeys a large deviation principle, $ρ_N \left(r-r_N^* \right) \asymp {e^{ - {N^ξ}I\left( {r- r_N^* } \right)}}$, where the rate function $I$ is convex and possesses its unique minimum at $r=r_N^*$, and $ξ$ is an exponent that scales $ρ_N$'s with $N$. We show that $ξ=1$ for Poisson random graphs, and $ξ\geq1$ for scale-free networks in which $ξ$ is a decreasing function of the degree distribution exponent $γ$. Our results reveal that the fluctuations of $r$ exhibits an anomalous scaling with $N$ in highly heterogeneous networks.

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arXiv2021

Random walks on complex networks with first-passage resetting

We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits either of observable nodes. We derive exact expressions of the stationary occupation probability, the average number of resets in the long time, and the mean first-passage time between arbitrary two non-observable nodes. We show that all the quantities can be expressed in terms of the fundamental matrix $\textbf{Z}=(\textbf{I}-\textbf{Q})^{-1}$, where $\textbf{I}$ is the identity matrix and $\textbf{Q}$ is the transition matrix between non-observable nodes. Finally, we use ring networks, 2d square lattices, barbell networks, and Cayley trees to demonstrate the advantage of first-passage resetting in global search on such networks.

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arXiv2021

Random walks on complex networks with multiple resetting nodes: a renewal approach

Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting nodes. Using a renewal approach, we derive exact expressions of the occupation probability of the walker in each node and mean-field first-passage time between arbitrary two nodes. All the results are relevant to the spectral properties of the transition matrix in the absence of resetting. We demonstrate our results on circular networks, stochastic block models, and Barabási-Albert scale-free networks, and find the advantage of the resetting processes to multiple resetting nodes in global searching on such networks.

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arXiv2020

Non-Markovian Majority-Vote model

Non-Markovian dynamics pervades human activity and social networks and it induces memory effects and burstiness in a wide range of processes including inter-event time distributions, duration of interactions in temporal networks and human mobility. Here we propose a non-Markovian Majority-Vote model (NMMV) that introduces non-Markovian effects in the standard (Markovian) Majority-Vote model (SMV). The SMV model is one of the simplest two-state stochastic models for studying opinion dynamics, and displays a continuous order-disorder phase transition at a critical noise. In the NMMV model we assume that the probability that an agent changes state is not only dependent on the majority state of his neighbors but it also depends on his {\em age}, i.e. how long the agent has been in his current state. The NMMV model has two regimes: the aging regime implies that the probability that an agent changes state is decreasing with his age, while in the anti-aging regime the probability that an agent changes state is increasing with his age. Interestingly, we find that the critical noise at which we observe the order-disorder phase transition is a non-monotonic function of the rate $β$ of the aging (anti-aging) process. In particular the critical noise in the aging regime displays a maximum as a function of $β$ while in the anti-aging regime displays a minimum. This implies that the aging/anti-aging dynamics can retard/anticipate the transition and that there is an optimal rate $β$ for maximally perturbing the value of the critical noise. The analytical results obtained in the framework of the heterogeneous mean-field approach are validated by extensive numerical simulations on a large variety of network topologies.

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