Fetching the paper…
Reading the bibliography…
We give a simple formula for the looping rate of loop-erased random walk on a finite planar graph.
I. Niven, Irrational numbers , Carus Mathematical Monographs #11, Mathematical Association of America, 1956
1956
Earlier work this paper cites.
F. Spitzer, Principles of random walks , second edition, Graduate Texts in Mathematics #34, Springer-Verlag, 1976
1976
Earlier work this paper cites.
C. J. Liu and Y. Chow, Enumeration of forests in a graph , Proc. Amer. Math. Soc. 83
1981
Earlier work this paper cites.
H. N. V. Temperley, Graph theory and applications , Ellis Horwood Series in Mathematics and its Applications, John Wiley & Sons, 1981
1981
Earlier work this paper cites.
S. Chaiken, A combinatorial proof of the all minors matrix tree theorem , SIAM J. Algebraic Discrete Methods 3
1982
Earlier work this paper cites.
G. Kalai, Enumeration of 𝐐 {\bf Q} -acyclic simplicial complexes , Israel J. Math. 45
1983
Earlier work this paper cites.
P. G. Doyle and J. L. Snell, Random walks and electric networks , Carus Mathematical Monographs #22, Mathematical Association of America, 1984
1984
Earlier work this paper cites.
P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality , Phys. Rev. A (3) 38
1988
Earlier work this paper cites.
D. Dhar, Self-organized critical state of sandpile automaton models , Phys. Rev. Lett. 64
1990
Earlier work this paper cites.
D. Dhar and S. N. Majumdar, Abelian sandpile model on the Bethe lattice , J. Phys. A 23
1990
Earlier work this paper cites.
S. N. Majumdar and D. Dhar, Height correlations in the abelian sandpile model , J. Phys. A: Math. Gen. 24
1991
Earlier work this paper cites.
R. Pemantle, Choosing a spanning tree for the integer lattice uniformly , Ann. Probab. 19
1991
Earlier work this paper cites.
S. N. Majumdar and D. Dhar, Equivalence between the abelian sandpile model and the q → 0 q\to 0 limit of the Potts model , Physica A 185
1992
Earlier work this paper cites.
W. Myrvold, Counting k k -component forests of a graph , Networks 22
1992
Cited alongside, same era.
R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances , Ann. Probab. 21
1993
Cited alongside, same era.
R. Forman, Determinants of Laplacians on graphs , Topology 32
1993
Cited alongside, same era.
V. B. Priezzhev, Exact height probabilities in the abelian sandpile model , Phys. Scr. T49
1993
Cited alongside, same era.
D. B. Wilson, Generating random spanning trees more quickly than the cover time , Proc. 28th Annual ACM Symposium on the Theory of Computing, 1996, pp. 296–303
1996
Cited alongside, same era.
C. Merino López, Chip firing and the Tutte polynomial , Ann. Comb. 1
O. Bernardi, Tutte polynomial, subgraphs, orientations and sandpile model: new connections via embeddings , Electron. J. Combin. 15
2008
Later among the works it cites.
2008
Later among the works it cites.
A. M. Duval, C. J. Klivans, and J. L. Martin, Simplicial matrix-tree theorems , Trans. Amer. Math. Soc. 361
2009
Later among the works it cites.
G. F. Lawler and V. Limic, Random walk: A modern introduction , Cambridge Studies in Advanced Mathematics #123, Cambridge Univ. Press, 2010
2010
Later among the works it cites.
V. S. Poghosyan and V. B. Priezzhev, The problem of predecessors on spanning trees , Acta Polytechnica 51
2011
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1997
Cited alongside, same era.
O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees , Israel J. Math. 118
2000
Cited alongside, same era.
I. Benjamini, R. Lyons, Y. Peres, and O. Schramm, Uniform spanning forests , Ann. Probab. 29
2001
Cited alongside, same era.
I. Benjamini and O. Schramm, Recurrence of distributional limits of finite planar graphs , Electron. J. Probab. 6
2001
Cited alongside, same era.
R. Cori and Y. Le Borgne, The sand-pile model and Tutte polynomials , Adv. in Appl. Math. 30
2003
Cited alongside, same era.
G. F. Lawler, O. Schramm, and W. Werner, Conformal invariance of planar loop-erased random walks and uniform spanning trees , Ann. Probab. 32
2004
Cited alongside, same era.
M. Jeng, G. Piroux, and P. Ruelle, Height variables in the abelian sandpile model: scaling fields and correlations , J. Stat. Mech. (2006), P10015
2006
Cited alongside, same era.
Later among the works it cites.
V. S. Poghosyan, V. B. Priezzhev, and P. Ruelle, Return probability for the loop-erased random walk and mean height in sandpile: a proof , J. Stat. Mech. (2011), P10004
2011
Later among the works it cites.
S. Caracciolo and A. Sportiello, Exact integration of height probabilities in the abelian sandpile model , J. Stat. Mech. Theory Exp. (2012), P09013
2012
Later among the works it cites.
D. Zeilberger, A combinatorial approach to matrix algebra , Discrete Math. 56
2013
Later among the works it cites.
2014
Closest in time.
A. A. Járai and N. Werning, Minimal configurations and sandpile measures , J. Theoret. Probab. 27
2014
Closest in time.
L. Levine and Y. Peres, The looping constant of ℤ d \mathbb{Z}^{d} , Random Structures Algorithms 45
2014
Closest in time.
R. Kenyon, Spanning forests and the vector bundle Laplacian , Ann. Probab. 39
2017
Closest in time.