For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state (i0, j0), we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive a certain integral representation for the probability of this event, and an asymptotic expression for the case when i0 becomes large, a situation in which the event beco...

Neighbor discovery is one of the emerging research areas in a wireless sensor network. After sensors are distributed, neighbor discovery is the first process to set up a communication channel with neighboring sensors. This paper proposes a new block design–based asymmetric neighbor discovery protocol for sensor networks. We borrow the concept of combinatorial block designs for our block combina...