  We study scenarii linked with the Swiss cheese picture in dimension three
obtained when two random walks are forced to meet often, or when one random
walk is forced to squeeze its range. In the case of two random walks, we show
that they most likely meet in a region of optimal density. In the case of one
random walk, we show that a small range is reached by a strategy uniform in
time. Both results rely on an original inequality estimating the cost of
visiting sparse sites, and in the case of one random walk on the precise Large
Deviation Principle of van den Berg, Bolthausen and den Hollander, including
their sharp estimates of the rate functions in the neighborhood of the origin
