Subdiffusive concentration in first passage percolation

We prove exponential concentration in i.i.d. first-passage percolation in Z^d for all dimensions  (greater than 1) and general edge-weights. These results extend work of Benaim-Rossignol to general distributions.

[1]  J. Hammersley,et al.  First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory , 1965 .

[2]  D. Huse,et al.  Pinning and roughening of domain walls in Ising systems due to random impurities. , 1985, Physical review letters.

[3]  H. Kesten.  Aspects of first passage percolation , 1986 .

[4]  On the critical behavior of the first passage time in d≥3 , 1991 .

[5]  H. Kesten.  On the Speed of Convergence in First-Passage Percolation , 1993 .

[6]  M. Talagrand.  Concentration of measure and isoperimetric inequalities in product spaces , 1994, math/9406212.

[7]  M. Talagrand.  On Russo's Approximate Zero-One Law , 1994 .

[8]  M. Ledoux.  On Talagrand's deviation inequalities for product measures , 1997 .

[9]  Double Behavior of Critical First-Passage Percolation , 1999 .

[10]  Christian Houdré,et al.  A converse Gaussian Poincaré-type inequality for convex functions , 1999 .

[11]  M. Ledoux.  The concentration of measure phenomenon , 2001 .

[12]  P. MassartLedoux,et al.  Concentration Inequalities Using the Entropy Method , 2002 .

[13]  First Passage Percolation Has Sublinear Distance Variance , 2002, math/0203262.

[14]  C. D. Howard,et al.  Models of First-Passage Percolation , 2004 .

[15]  Michel Benaim,et al.  Exponential concentration for first passage percolation through modified Poincaré inequalities , 2006, math/0609730.

[16]  Dvir Falik,et al.  Edge-Isoperimetric Inequalities and Influences , 2007, Comb. Probab. Comput..

[17]  Nathaniel D. Blair-Stahn,et al.  First passage percolation and competition models , 2010, 1005.0649.

[18]  Noise sensitivity and percolation , 2011 .

[19]  G. Grimmett,et al.  Percolation since Saint-Flour , 2012, 1207.0373.

[20]  S. Boucheron,et al.  Concentration inequalities : a non asymptotic theory of independence , 2013 .

[21]  Subgaussian concentration and rates of convergence in directed polymers , 2012, 1204.1819.

[22]  M. Damron,et al.  Rate of convergence in first-passage percolation under low moments , 2014, 1406.3105.

[23]  M. Damron,et al.  GAUSSIAN CONCENTRATION FOR THE LOWER TAIL IN FIRST-PASSAGE PERCOLATION UNDER LOW MOMENTS , 2014 .

[24]  S. Sodin.  Positive Temperature Versions of Two Theorems on First-Passage Percolation , 2013, 1301.7040.

[25]  S. Chatterjee.  Superconcentration and Related Topics , 2014 .

[26]  M. Damron,et al.  Sublinear variance in first-passage percolation for general distributions , 2013, 1306.1197.