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For an infinite Coxeter system, one can extend the weak right order to theset of infinite reduced words. This is called limit weak order. In[Transformation Groups 18(1), 2013, 179-231], Lam and Pylyavskyy showed thatfor affine Weyl groups of type $\widetilde{A}_n$ minimal infinite reduced wordsunder the limit weak order are precisely those infinite Coxeter elements andasked the question of characterization, in terms of infinite reduced words, ofthe minimal elements of the limit weak order for other affine types. In thispaper, we answer this question by characterizing the minimal infinite reducedwords for other irreducible affine Weyl groups by one of their reducedexpressions.

Reduced expression of minimal infinite reduced words of affine Weyl groups