We consider the dynamics of lattice random walks with resetting. The walker moving
randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a …

Exploiting powerful techniques from physics and mathematics, this book studies animal
movement in ecology, with a focus on epidemic spread. Pulmonary syndrome is not only …

A lattice random walk is a mathematical representation of movement through random steps
on a lattice at discrete times. It is commonly referred to as Pólya's walk when the steps occur …

This book provides a graduate-level introduction to three powerful and closely related
techniques in condensed matter physics: memory functions, projection operators, and the …

The ability to quantify when and where animals interact is key to the understanding of a
plethora of ecological processes, from the structure of social communities and predator–prey …

Random transmission events between individuals occurring at short scales control patterns
emerging at much larger scales in natural and artificial systems. Examples range from the …

We consider a random walker whose motion is tethered around a focal point. We use two
models that exhibit the same spatial dependence in the steady state but widely different …

Explicit solutions are presented in the Laplace and time domains for a one-variable Fokker–
Planck equation governing the probability density of a random walker moving in a confining …

The process of transmission of infection in epidemics is analyzed by studying a pair of
random walkers, the motion of each of which in two dimensions is confined spatially by the …

A particle roaming in a potential in the presence of spatial heterogeneities such as traps or
physical barriers is a mathematical representation of a vast number of processes across …