Random walks on networks: cumulative distribution of cover time
Nikola Zlatanov, Ljupco Kocarev
TL;DR
This paper derives exact and approximate formulas for the distribution of cover time in random walks on arbitrary graphs, providing insights into how long it takes to visit all nodes.
Contribution
It presents a novel exact analytical expression for cover time distribution on any graph and an efficient approximation method with practical computational complexity.
Findings
Exact cover time distribution formulas for specific graph types
An approximation method with O(2^n) complexity tested on graphs with up to 1000 nodes
Validation of the approximation's accuracy through numerical testing
Abstract
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n), is also presented. The approximation is numerically tested only for graphs with n<=1000 nodes.
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