相关论文: Flips Reveal the Universal Impact of Memory on Ran…

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…

These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…

It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…

Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its…

We consider quantum jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time…

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…

We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…

Free recall of random lists of words is a standard paradigm used to probe human memory. We proposed an associative search process that can be reduced to a deterministic walk on random graphs defined by the structure of memory…

We consider random walks, say $W_n=(M_0, M_1,\dots, M_n)$, of length $n$ starting at 0 and based on the martingale sequence $M_k$ with differences $X_m=M_m-M_{m-1}$. Assuming that the differences are bounded, $|X_m|\leq 1$, we solve the…

We study discrete quantum dynamics where single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often non-Markovian memory effects are attributed to structured environments…

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…

We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…

We study how memory impacts passages at the origin for a so-called elephant random walk in the diffusive regime. We observe that the number of zeros always grows asymptotically like the square root of the time, despite the fact that,…

The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

One of the main challenges in reinforcement learning is solving tasks with sparse reward. We show that the difficulty of discovering a distant rewarding state in an MDP is bounded by the expected cover time of a random walk over the graph…