Transversal fluctuations for a first passage percolation model
  We introduce a new first passage percolation model in a Poissonian environment on $\mathbb{R}^{2}$. In this model, the action of a path depends on the geometry of the path and the travel time. We prove that the transversal fluctuation exponent for point-to-line action minimizers is at least $3/5$. 
Yuri Bakhtin, Wei Wu
math.PR