Three-Step and Four-Step Random Walk Integrals

Three-Step and Four-Step Random Walk Integrals

We investigate the moments of 3-step and 4-step uniform random walk in the plane. In particular, we further analyse a formula conjectured in [BNSW09] expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W4(±1) are given and two new conjectures are recorded.

Random Walk Integrals

We study the expected distance of a two-dimensional walk in the plane with unit steps in random directions. A series evaluation and recursions are obtained making it possible to explicitly formulate this distance for small number of steps. Closed form expressions for all the moments of a 2-step and a 3-step walk are given, and a formula is conjectured for the 4-step walk. Heavy use is made of t...

Step-by-Step Random Walk Network with Power-Law Clique-Degree Distribution

Distribution ∗ YANG Han-Xin( )1∗∗, WANG Bing-Hong( )1,3∗∗∗, LIU Jian-Guo( ), HAN Xiao-Pu( ), ZHOU Tao( ) Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei 230026 Department of Physics, University of Fribourg, Chemin du Muse 3, CH-1700 Fribourg, Switzerland Institute of Complex Adaptive System, Shanghai Academy of System Science, Shan...

Entanglement swapping via three-step quantum walk-like protocol

We present an entanglement swapping process for unknown nonmaximally entangled photonic states, where the standard Bell-state measurement is replaced by a three-step quantum walk-like state discrimination process, i.e., the practically nontrivial coupling element of two photons is replaced by manipulating their trajectories, which will greatly enrich the dynamics of the coupling between photons...

The Four Step Model