Related papers: Possible Connection between the Optimal Path and F…
We present a calculation of the weak localisation correction to the scattering and to the transport mean free path, for waves propagating in a $delta$-correlated random potential, going beyond the usual diffusion approximation for the loops…
The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized,…
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the…
We study the distribution of maximal-chain lengths between two elements of a causal set and its relationship with the embeddability of the causal set in a region of flat spacetime. We start with causal sets obtained from uniformly…
In this note, we study the model of directed last passage percolation on $\mathbb{Z}^2$, with i.i.d. exponential weight. We consider the maximum paths from vertices $\left(0,\lfloor k^{2/3} \rfloor\right)$ and $(\lfloor k^{2/3} \rfloor,0)$…
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…
Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two…
In last passage percolation models lying in the Kardar-Parisi-Zhang universality class, maximizing paths that travel over distances of order $n$ accrue energy that fluctuates on scale $n^{1/3}$; and these paths deviate from the linear…
We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied,…
Packet networks need to maintain state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or…
Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic…
Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered…
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of…
Diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations and the expression for the passing probability is obtained exactly. The passing probability is…