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We consider the simple random walk on a random d-regular graph with n vertices, and investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. It was shown in [ ˇ CTW11] that this so-called vacant set exhibits a phase transition at u = u : there is a giant component if u < u… (More)

- Andrew F Schwerin, Justin C Johnson, Millicent B Smith, Paiboon Sreearunothai, Duska Popović, Jirí Cerný +10 others
- The journal of physical chemistry. A
- 2010

Single crystal molecular structure and solution photophysical properties are reported for 1,3-diphenylisobenzofuran (1), of interest as a model compound in studies of singlet fission. For the ground state of 1 and of its radical cation (1(+*)) and anion (1(-*)), we report the UV-visible absorption spectra, and for neutral 1, also the magnetic circular… (More)

We study the simple random walk on the n-dimensional hypercube, in particular its hitting times of large (possibly random) sets. We give simple conditions on these sets ensuring that the properly-rescaled hitting time is asymptotically exponentially distributed, uniformly in the starting position of the walk. These conditions are then verified for… (More)

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