Abstract
We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of movements of the walker. Applying the saddle point method, we reveal that the scaling limit gives the Tracy-Widom distribution, which is the same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.
Original language | English |
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Pages (from-to) | 3033-3048 |
Number of pages | 16 |
Journal | Journal of Physics A: Mathematical and General |
Volume | 36 |
Issue number | 12 SPEC. ISS. |
DOIs | |
Publication status | Published - Mar 28 2003 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)