Complexity of zigzag sampling algorithm for strongly log-concave distributions

We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves varepsilon error in chi-square divergence with a computational cost equivalent to Obigl(kappa2 d^frac12(logfrac1varepsilon)^frac32bigr) gradient evaluations in the regime kappa ll fracdlog d under a warm start assumption, where kappa is the condition number and d is the dimension.