22 citations · 143 across the 51 of their papers we have counts for
9 papers · 1 filter
Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings
David A. Croydon, Makiko Sasada, Satoshi Tsujimoto
We define bi-infinite versions of four well-studied discrete integrable models, namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation,…
Anomalous scaling regime for one-dimensional Mott variable-range hopping
David A. Croydon, Ryoki Fukushima, Stefan Junk
We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional dif…
Discrete integrable systems and Pitman's transformation
David A. Croydon, Makiko Sasada
We survey recent work that relates Pitman's transformation to a variety of classical integrable systems, including the box-ball system, the ultra-discrete and discrete KdV equation…
Detailed balance and invariant measures for discrete KdV- and Toda-type systems
David A. Croydon, Makiko Sasada
In order to study the invariant measures of discrete KdV- and Toda-type systems, this article focusses on models, discretely indexed in space and time, whose dynamics are determini…
An introduction to the trapping experienced by biased random walk on the trace of biased random walk
David A. Croydon
We introduce and summarise results from the recent paper 'Biased random walk on the trace of biased random walk on the trace of ...', which was written jointly with M. P. Holmes (U…
The random conductance model with heavy tails on nested fractal graphs
David A. Croydon
Recently, Kigami's resistance form framework has been applied to provide a general approach for deriving the scaling limits of random walks on graphs with a fractal scaling limit.…