Related papers: Some reflections on directed lattice paths
We consider a self-avoiding walk on the $d$-dimensional hypercubic lattice, terminally attached to an impenetrable hyperplane at which it can adsorb. When a force is applied the walk can be pulled off the surface and we consider the…
We study a random walk (Markov chain) in an unbounded planar domain whose boundary is described by two curves of the form $x_2 = a^+ x_1^{\beta^+}$ and $x_2 = -a^- x_1^{\beta^-}$, with $x_1 \geq 0$. In the interior of the domain, the random…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Lattice paths effectively model phenomena in chemistry, physics and probability theory. Asymptotic enumeration of lattice paths is linked with entropy in the physical systems being modeled. Lattice paths restricted to different regions of…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
We consider walks on the edges of the square lattice $\mathbb Z^2$ which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in another direction. We classify these rules according to a…
A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately achieves first-passage, leaving the medium or it is absorbed. The Kubelka-Munk model describes a…
The reflected process of a random walk or L\'evy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves…
We analyse some enumerative and asymptotic properties of lattice paths below a line of rational slope. We illustrate our approach with Dyck paths under a line of slope $2/5$. This answers Knuth's problem #4 from his "Flajolet lecture"…
We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda_i) of the fluid's components. In any plane perpendicular to the contact…
Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a…
The study of lattice walks restricted to the first quadrant has shed a lot of interest in the past twenty years. In particular, there has been an important effort to classify models of weighted walks with small steps with respect to the…
A discrete implementation on a lattice of the Active Walker Model is presented. After the model's validity is shown in simple simulations, more complex simulations of walkers passing consecutively a lattice from an arbitrary starting point…
Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…
This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic,…
In 2010 Banderier and Nicodeme consider the height of bounded discrete bridges and conclude to a limiting Rayleigh distribution. This result is correct although their proof is partly erroneous. They make asymptotic simplifications based…
We consider a self-avoiding walk model of polymer adsorption where the adsorbed polymer can be desorbed by the application of a force. In this paper the force is applied normal to the surface at the last vertex of the walk. We prove that…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
We analyze response of a macromolecule near to a substrate; the substrate is tiled in the sequential and specific manner so that repeat units of the macromolecule may have different response on its adsorption in different directions onto…