Download e-book for kindle: A Guide to First-Passage Processes by Sidney Redner

By Sidney Redner

ISBN-10: 0521036917

ISBN-13: 9780521036917

ISBN-10: 0521652480

ISBN-13: 9780521652483

First-passage homes underlie quite a lot of stochastic techniques, equivalent to diffusion-limited development, neuron firing, and the triggering of inventory recommendations. This ebook presents a unified presentation of first-passage strategies, which highlights its interrelations with electrostatics and the ensuing strong effects. the writer starts off with a contemporary presentation of basic idea together with the relationship among the career and first-passage chances of a random stroll, and the relationship to electrostatics and present flows in resistor networks. the results of this thought are then built for easy, illustrative geometries together with the finite and semi-infinite durations, fractal networks, round geometries and the wedge. numerous functions are provided together with neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin structures, and the kinetics of diffusion-controlled reactions. Examples mentioned contain neuron dynamics, self-organized criticality, kinetics of spin platforms, and stochastic resonance.

Show description

Read Online or Download A Guide to First-Passage Processes PDF

Best stochastic modeling books

Read e-book online Disorder in Physical Systems: A Volume in Honour of John PDF

On 21 March 1990 John Hammersley celebrates his 70th birthday. a few his colleagues and associates desire to pay tribute in this get together to a mathematician whose remarkable inventiveness has tremendously enriched mathematical technological know-how. The breadth and flexibility of Hammersley's pursuits are striking, doubly so in an age of elevated specialisation.

Read e-book online An Elementary Introduction To Stochastic Interest Rate PDF

Rate of interest modeling and the pricing of similar derivatives stay topics of accelerating value in monetary arithmetic and threat administration. This ebook offers an available advent to those subject matters by way of a step by step presentation of recommendations with a spotlight on particular calculations. each one bankruptcy is observed with routines and their entire options, making the e-book compatible for complicated undergraduate and graduate point scholars.

Get Coupling, Stationarity, and Regeneration PDF

This can be a ebook on coupling, together with self-contained remedies of stationarity and regeneration. Coupling is the principal subject within the first 1/2 the e-book, after which enters as a device within the latter part. the 10 chapters are grouped into 4 components.

Extra resources for A Guide to First-Passage Processes

Sample text

Paradoxically, although every site is visited with certainty, these visitations take forever because the mean time to return to the origin, (t) = f t F(0, Odt, diverges for all d < 2. On the other hand, for d > 2, Eq. 8) predicts that there is a nonzero probability for a diffusing particle to not return to its starting point. More 24 First-Passage Fundamentals generally, there is a nonzero probability for a random walk to miss most of the lattice sites. This incomplete visitation follows from the density of visited sites p within the exploration sphere tending to zero as t oo.

5. 4 to determine the time dependence of the first-passage probability in terms of the generating function for the occupation probability. For simplicity, consider an isotropic random walk that starts at the origin. From the Gaussian probability distribution given in Eq. 27), P(17 0, t) = (471 DO —d / 2 in d dimensions. Then Eq. 1) gives the corresponding generating function: - P(0, z) P(0, t) z` dt cc On- Dtr d i 2 z t dt. 4, this integral has two fundamentally different behaviors, depending on whether fc° P(0, t)dt diverges or converges.

20) with the boundary conditions t(x_ ) t(x + ) = 0, which correspond to the exit time being equal to zero if the particle starts at the boundary. This recursion relation expresses the mean exit time starting at x in terms of the outcome one step in the future, for which the initial walk can be viewed as restarting at either x + 8x or at x — 8x, each with probability 1/2, but also with the time incremented by (St. In the continuum limit, the Taylor expansion of this recursion formula to lowest nonvanishing order yields the Poisson equation Dt"(x) = —1.

Download PDF sample

A Guide to First-Passage Processes by Sidney Redner

by Daniel

Rated 4.11 of 5 – based on 36 votes