# Random walks in noninteger dimension

@article{Bender1994RandomWI, title={Random walks in noninteger dimension}, author={C. Bender and S. Boettcher and L. Mead}, journal={Journal of Mathematical Physics}, year={1994}, volume={35}, pages={368-388} }

One can define a random walk on a hypercubic lattice in a space of integer dimension D. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given number of time steps. These formulas are physically meaningful for integer values of D. However, these formulas are unacceptable as probabilities when continued to noninteger D because they give values that can be greater than 1 or less than 0. In this paper a… CONTINUE READING

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