We show that residence time measures can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one-dimensional simple random walk. The sites of the lattice are regular, i.e., the jumping probabilities are the same in each site, except for a site, called defect, where the jumping probabilities are different. At each side of the lattice an absorbing site is present. We show that by measuring the fraction of particles crossing the channel and/or the typical time they need to cross it, it is possible to identify the main features of the lattice and of the defect site, namely, the jumping probabilities at the regular and at the defect site and the position of the defect in the lattice.


  1. defect localization
  2. random walk
  3. residence time

MSC codes

  1. 60G50
  2. 60J74
  3. 82B41

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Supplementary Material

PLEASE NOTE: These supplementary files have not been peer-reviewed.

Index of Supplementary Materials

Title of paper: Localization of Defects via Residence Time Measures

Authors: A. Ciallella, E.N.M. Cirillo, and B. Vantaggi

File: M138028SupMat.pdf

Type: PDF

Contents: An appendix to the paper describing the construction of the Generating function for the specific problem studied.


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Information & Authors


Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 502 - 525
ISSN (online): 1095-712X


Submitted: 17 November 2020
Accepted: 25 October 2021
Published online: 24 March 2022


  1. defect localization
  2. random walk
  3. residence time

MSC codes

  1. 60G50
  2. 60J74
  3. 82B41



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