Profile of Yuval Peres
نویسندگان
چکیده
منابع مشابه
The Looping Constant of Z Lionel Levine and Yuval Peres
The looping constant ξ(Z) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Z. Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilson, proved recently that ξ(Z) = 54 . We consider the infinite volume limits as G ↑ Z of three different statistics: (1) The expected length of the cycle in a uniform spanning unicycle of G; (2) The e...
متن کاملIs the Looping Constant of the Square Grid 5/4? Lionel Levine and Yuval Peres
We define a quantity called the looping constant of the integer lattice Z, and conjecture that its value for Z is 5/4. A number of striking numerical facts would follow: (1) The first derivative in y of the Tutte polynomial of the N ×N square grid graph GN , evaluated at x = y = 1 and divided by N, has the limiting value 1/8 as N →∞; (2) The expected density of a uniform recurrent state of the ...
متن کاملConvolutions of Cantor Measures without Resonance Fedor Nazarov, Yuval Peres and Pablo Shmerkin
Denote by μa the distribution of the random sum (1 − a)∞j=0 ωja , where P(ωj = 0) = P(ωj = 1) = 1/2 and all the choices are independent. For 0 < a < 1/2, the measure μa is supported on Ca, the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length (1 − 2a), and iterating this process inductively on each of the remaining intervals. We...
متن کاملCritical Random Graphs: Diameter and Mixing Time Asaf Nachmias and Yuval Peres
Let C1 denote the largest connected component of the critical ErdősRényi random graph G(n, 1 n ). We show that, typically, the diameter of C1 is of order n and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald [5]. These results extend to clusters of size n of p-bond percolation on any d-regular n-vertex graph where...
متن کاملRecurrent graphs where two independent random walks collide finitely often Manjunath Krishnapur and Yuval Peres
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z 2 by removing all horizontal edges off the x-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2018
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1813856115