Abstract
We give nontrivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions and verify a conjecture of Benjamini, Kozma and Schapira. To the best of our knowledge, these are the first nontrivial results for this two-dimensional model.
Funding Statement
Omer Angel was funded, in part, by NSERC.
Mark Holmes was supported by Future Fellowship FT160100166 from the Australian Research Council.
Alejandro Ramírez has been partially supported by Fondecyt 1180259 and by Iniciativa Científica Milenio.
Citation
Omer Angel. Mark Holmes. Alejandro Ramirez. "Balanced excited random walk in two dimensions." Ann. Probab. 51 (4) 1421 - 1448, July 2023. https://doi.org/10.1214/23-AOP1622
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