Related papers: The shape of a memorised random walk
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
Random walks on lattices with preferential relocation to previously visited sites provide a simple framework for modeling the displacements of animals and humans. When the lattice contains a few impurities or resource sites where the walker…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Principles of self-organization play an increasingly central role in models of human activity. Notably, individual human displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically…
The monkey walk is a stochastic process defined as the trajectory of a walker that moves on $\mathbb R^d$ according to a Markovian generator, except at some random "relocation" times at which it jumps back to its position at a time sampled…
What people choose to see, like, or remember is of profound interest to city planners and architects. Previous research suggests what people are more likely to store in their memory - buildings with dominant shapes and bright colors,…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Human memory retrieval often resembles ecological foraging where animals search for food in a patchy environment. Optimal foraging means following the Marginal Value Theorem (MVT), in which individuals exploit a patch of semantically…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…
We present a simple model of a random walk with partial memory, which we call the \emph{random memory walk}. We introduce this model motivated by the belief that it mimics the behavior of the once-reinforced random walk in high dimensions…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
The rates at which individuals memorize and forget environmental information strongly influence their movement paths and long-term space use. To understand how these cognitive time scales shape population-level patterns, we propose and…