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We study the effect of a large obstacle on the so called residence time,i.e., the time that a particle performing a symmetric random walk in arectangular (2D) domain needs to cross the strip. We observe a complexbehavior, that is we find out that the residence time does not dependmonotonically on the geometric properties of the obstacle, such as its width,length, and position. In some cases, due to the presence of the obstacle, themean residence time is shorter with respect to the one measured for theobstacle--free strip. We explain the residence time behavior by developing a 1Danalog of the 2D model where the role of the obstacle is played by two defectsites having a smaller probability to be crossed with respect to all the otherregular sites. The 1D and 2D models behave similarly, but in the 1D case we areable to compute exactly the residence time finding a perfect match with theMonte Carlo simulations.

Residence time of symmetric random walkers in a strip with large reflective obstacles