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- W4200463944 abstract "Abstract We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of N nodes of degree c ( c ⩾ 3). Starting from a random initial node at time t = 1, at each time step t ⩾ 2 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may visit a new, yet-unvisited node, while in other time steps it may revisit a node that has already been visited before. The cover time T C is the number of time steps required for the RW to visit every single node in the network at least once. We derive a master equation for the distribution P t ( S = s ) of the number of distinct nodes s visited by an RW up to time t and solve it analytically. Inserting s = N we obtain the cumulative distribution of cover times, namely the probability P ( T C ⩽ t ) = P t ( S = N ) that up to time t an RW will visit all the N nodes in the network. Taking the large network limit, we show that P ( T C ⩽ t ) converges to a Gumbel distribution. We calculate the distribution of partial cover (PC) times P ( T PC, k = t ), which is the probability that at time t an RW will complete visiting k distinct nodes. We also calculate the distribution of random cover (RC) times P ( T RC, k = t ), which is the probability that at time t an RW will complete visiting all the nodes in a subgraph of k randomly pre-selected nodes at least once. The analytical results for the distributions of cover times are found to be in very good agreement with the results obtained from computer simulations." @default.
- W4200463944 created "2021-12-31" @default.
- W4200463944 creator A5052596738 @default.
- W4200463944 creator A5078368781 @default.
- W4200463944 creator A5079919630 @default.
- W4200463944 date "2021-12-08" @default.
- W4200463944 modified "2023-10-17" @default.
- W4200463944 title "Analytical results for the distribution of cover times of random walks on random regular graphs" @default.
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- W4200463944 doi "https://doi.org/10.1088/1751-8121/ac3a34" @default.
- W4200463944 hasPublicationYear "2021" @default.
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