Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation
Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation
This monograph resolves—in a dense class of cases—several open problems concerning geodesics in i.i.d. first-passage percolation on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper Z Superscript d"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {Z}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our primary interest is in the empirical measures of …