  We consider last passage percolation (LPP) models with exponentially
distributed random variables, which are linked to the totally asymmetric simple
exclusion process (TASEP). The competition interface for LPP was introduced and
studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 1235-1254] for
cases where the corresponding exclusion process had a rarefaction fan. Here we
consider situations with a shock and determine the law of the fluctuations of
the competition interface around its deterministic law of large number
position. We also study the multipoint distribution of the LPP around the
shock, extending our one-point result of [Probab. Theory Relat. Fields 61
(2015), 61-109].
