We consider a discrete-time continuous-space random walk under the
constraints that the number of returns to the origin (local time) and the total
area under the walk are fixed. We first compute the joint probability of an
excursion having area a and returning to the origin for the first time after
time τ. We then show how condensation occurs when the total area
constraint is increased: an excursion containing a finite fraction of the area
emerges. Finally we show how the phenomena generalises previously studied cases
of condensation induced by several constraints and how it is related to
interaction-driven condensation which allows us to explain the phenomenon in
the framework of large deviation theory.Comment: 28 pages, 6 figures, invited paper for Special Issue of J. Phys. A
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