Fluctuations of recentered maxima of discrete Gaussian Free Fields on a class of recurrent graphs

On the cycle maximum of birth-death processes and networks of queues

This paper considers the cycle maximum in birth-death processes as a stepping stone to characterisation of the cycle maximum in single queues and open Kelly-Whittle networks of queues. For positive recurrent birth-death processes we show that the sequence of sample maxima is stochastically compact. For transient birth-death processes we show that the sequence of sample maxima conditioned on the maximum being finite is stochastically compact. We show that the Markov chain recording the total number of customers in a Kelly-Whittle network is a birth-death process with birth and death rates deter…