branching random walkreceding boundaryprinciple of a single big jumpProceedings of the Steklov Institute of Mathematics - Foss and Zachary (2003) and Foss, Palmowski and Zachary (2005) studied the probability of achieving a receding boundary on a time interval of......
under our ballisticity criterion the quenched probability of reaching a point far away is lower bounded. the second section is sect. 5.2 , in which we recall some classical results from rwres. finally the third part is sect. 5.3 , in which we finish the proof by providing an ...
In case the density of the random walkers is reaching a steady state, its value at a given node can be interpreted as the probability that the node was the source of information. Consequently, high random walker density values indicate a high standing in the hierarchy, whereas low density ...
•Givenanundirected,connectedgraphG(V,E)with|V|=n,|E|=marandom“step”inGisamovefromsomenodeutoarandomlyselectedneighborv.Arandomwalkisasequenceoftheserandomstepsstartingfromsomeinitialnode.5 43 6 2 1G Pointstonote •Processesisdiscrete•Gisnotnecessarilyplanar•Gisnotnecessarilyfullyconnected•A...
•Givenanundirected,connectedgraphG(V,E)with|V|=n,|E|=marandom“step”inGisamovefromsomenodeutoarandomlyselectedneighborv.Arandomwalkisasequenceoftheserandomstepsstartingfromsomeinitialnode.5 43 6 2 1G Pointstonote •Processesisdiscrete•Gisnotnecessarilyplanar•Gisnotnecessarilyfullyconnected•A...
Socioeconomic segregation has an important role in the emergence of large-scale inequalities in urban areas. Most of the available measures of spatial segregation depend on the scale and size of the system under study, or neglect large-scale spatial corr
A random walk in $Z_+^2$ spatially homogeneous in the interior, absorbed at the axes, starting from an arbitrary point $(i_0,j_0)$ and with step probabilities drawn on Figure 1 is considered. The trivariate generating function of probabilities that the random walk hits a given point $(...
A random walk is basically looking at the time sequence in a binomial process. We will only consider the simplest random walks here … Random Walk in 1-D Consider an asymmetric random walk along the x-axis, beginning at the origin. There is a probability p that the step will be +1, ...
Run code for 10 million iterationspython3 ./random-walk-graph.py Solution This assumes a random choice from a uniform distribution is being made at every intersection. Probability of reaching green is0.111036211104or(1/9). If we consider the node at the symmetry of graph, i.e., the node ...
We now describe the model of a biased random walk on a subcritical GW-tree conditioned to survive which will be the main focus of the article. Let \(f(s):=\sum _{k=0}^\infty p_ks^k\) denote the probability generating function of the offspring law of a GW-process with mean \(\...