# Rob van den Berg's CWI Homepage


Name        Prof.dr. J. (Rob) van den Berg
Science Park 123
NL 1098 XG Amsterdam
The Netherlands
Telephone   +31 20 5924008
E-mail      jvdberg at cwidotnl


My main field of interest is probability theory, in particular percolation, interacting particle systems and other random spatial processes. I work as a researcher at CWI in the group Stochastics
and as professor (part-time:0.2 fte) at the VU University Amsterdam.

## Publications

J. van den Berg and D.G.P. van Engelenburg, An upper bound on the two-arms exponent for critical percolation on Z^d,
arXiv:2009.13337 (10 pages). Link to arXiv
To appear (in revised form) in Ann. Inst. H. Poincar\'e Probab. Statist.

J. van den Berg and P. Nolin, On the four-arm exponent for 2D percolation at criticality,
In: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius , pp 125-145,
(Vares, M.E., Fernandez, R., Fontes, L.R., Newman, C.M. (Eds.)),
Series Progress in Probability 77, Springer, 2021. Link to final version Link to arXiv version

J. van den Berg and H. Don, A lower bound for point-to-point connection probabilities in critical percolation,
Electron. Comm. Probab. 25, paper 47 (2020) Link to article

J.van den Berg and P. Nolin, Near-critical percolation with heavy-tailed impurities, forest fires and frozen percolation,
To appear in PTRF (2021). Link to `Online First'

J. van den Berg and S.A. Bethuelsen, Stochastic Domination in Space-Time for the Contact Process,
Random Structures and Algorithms 53, 221-237 (2018). Link to arXiv Link to article

J. van den Berg, D. Kiss and P. Nolin, Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters,
Annales Scientifiques de l'\'Ecole Normale Sup\'erieure 51, 1017--1084 (2018). Link to article Link to arXiv

J. van den Berg and P. Nolin, Boundary rules and breaking of self-organized criticality in 2D frozen percolation,
Electron. Comm. Probab. 22 (2017), paper no. 65, 15 pp. Link to article

J. van den Berg and P. Nolin, Two-dimensional volume-frozen percolation: Exceptional scales,
Annals of Applied Probability 27, 91-108 (2017). Link to article

J. van den Berg and R. Conijn, The expected number of critical percolation clusters intersecting a line segment,
Electron. Commun. Probab. 21, no. 28, 1-10 (2016). article

J. van den Berg, J. Björnberg, and M. Heydenreich, Sharpness versus robustness of the percolation transition in 2D contact processes
Stochastic Processes and their Applications 125, 513–-537 (2015). Link to article Link to arXiv

J. van den Berg and A. Gandolfi, BK-type inequalities and generalized random-cluster representations,
Probability Theory and Related Fields 157, 157-181 (2013). Article

J. van den Berg and R. Conijn, The gaps between the sizes of large clusters in $2D$ critical percolation,
Electronic Communictions in Probability 18, paper 92, 1-9 (2013). Link to article

On the size of the largest cluster in $2D$ critical percolation (with R. Conijn),
Electr. Comm. Probab. 17, Art.nr. 58 (2012). Link to article

J. van den Berg, B.N.B. de Lima and P. Nolin, A percolation process on the square lattice where large finite clusters are frozen,
Random Structures and Algorithms 40, 220-226 (2012). Link to article Link to arXiv"

J. van den Berg, D. Kiss and P. Nolin, A percolation process on the binary tree where large finite clusters are frozen,
Electronic Communications in Probability 17, no. 2 (2012). Link to article

J. van den Berg and D. Kiss, Sublinearity of the travel-time variance for dependent first passage percolation,
Ann. Probab. 40, 743-764 (2012). Link to article

J. van den Berg and J. Jonasson, A BK inequality for randomly drawn subsets of fixed size,
Probability Theory and Related Fields, 154, 835-844 (2012). Link to article

Sharpness of the percolation transition in the two-dimensional contact process,
Ann. Appl. Probab. {\bf 21}, 374-395 (2011). Link to article

Escape of resources in a distributed clustering process,
(with M. Hilário and A. Holroyd)
Elect. Comm. Probab. 15, paper 40, 442-448 (2010). Article

Linear lower bounds for $\delta_c(p)$ for a class of $2D$ self-destructive percolation models,
(with B. de Lima),
Random Structures and Algorithms 34 (2009). Link to article Link to arXiv

J. van den Berg, Approximate zero-one laws and sharpness of the percolation transition in a class of models including 2D Ising percolation,
Annals of Probability 36, 1880-1903 (2008). Link to article

Random spatial growth with paralyzing obstacles,
(with Y. Peres, V. Sidoravicius and M.E. Vares),
Annales de l' Inst. H. Poincar\'e (B) Probab. et Stat. 44, 1173-1187 (2008). Link to article

Box-crossings and Continuity results for self-destructive percolation in the plane,
(with R. Brouwer and B. Vagvölgyi),
In and out of equilibrium 2 Series: Progress in probability vol. 60, V. Sidoravicius and M. Vares (Eds.), Birkh\"auser, pp. 117-136 (2008). Link to article

The size of a pond in $2D$ invasion percolation,
(with A. Járai and B. Vagvölgyi),
Elect. Comm. Probab. 12, 411-420 (2007). Article

J. van den Berg and R. Brouwer, Self-organized forest-fires near the critical time, Communications in Mathematical Physics 267, 265-277 (2006). Link to article Link to arXiv

Proof of a conjecture of N. Konno for the 1D contact process,
(with O. Häggström and J. Kahn),
Dynamic and stochastics, Festschrift in honor of M.S. Keane (D. Denteneer, F. den Hollander and E. Verbitskiy, eds.), {IMS Lecture Notes-Monograph Series} {\bf 48}, 16-23 (2006). Link to article

Some conditional correlation inequalities for percolation and related processes,
(with O. Häggström and J. Kahn),
Random Structures and Algorithms 29, 417-435 (2006). Link to article Link to arXiv

On the asymptotic density in a one-dimensional critical forest-fire model
(with A. Járai),
Comm. Math. Phys. 253, 633-644 (2005). Link to article

The lowest crossing in 2D critical percolation,
(with A. Járai),
Ann. Probab. 31, 1241-1253 (2003). Link to article

Self-destructive percolation
(with R. Brouwer),
Random Structures and Algorithms 24, 480-501 (2004). Link to article

Randomly coalescing random walks in dimension $d \ge 3$
(with H. Kesten),
In and Out of Equilibrium (V. Sidoravicius, ed.), 1-45, Birkhäuser. (2002) Link

A signal-recovery system: asymptotic properties, and construction of an infinite-volume process
(with B. Tóth)
Stoch. Proc. Appl. 96, 177-190 (2001). Link to article Link to arXiv version

A correlation inequality for connection events in percolation
(with J. Kahn),
Ann. Probab. 29, 123-126 (2001). Link to article

Random sampling for the monomer-dimer model on a lattice,
(with R. Brouwer),
J. Math. Phys. 41, 1585-1597 (March 2000). Link to article

J. van den Berg and H. Kesten,
Asymptotic density in a coalescing random walk model,
Annals of Probability 28, 303-352 (2000). Link to article

On the absence of phase transition in the monomer-dimer model (1999),
Perplexing problems in Probability (Festschrift in honor of Harry Kesten) 185-195, Birkhauser.

On the existence and non-existence of finitary codings for a class of random fields,
(with J. Steif),
Ann. Probab. 27, 1501-1522 (1999). Link to article

Dependent random graphs and spatial epidemics,
(with G. Grimmett and R. Schinazi),
Annals of Applied Probability 8, 317-336 (1998). Link to article

Dynamic Boolean models,
(with R. Meester and D. White),
Stochastic Processes and their Applications 69, 247-257 (1997). Link to article

A constructive mixing condition for 2-D Gibbs measures with random interactions,
Annals of Probability 25, 1316-1333 (1997). Link to article

A remark on the Van Lieshout and Baddeley J-function for point processes,
(with T. Bedford),

On a distributed clustering process of Coffman, Courtois, Gilbert and Piret,
(with A. Ermakov),
Journal of Applied Probability 35, 919--924 (1998). Link to article

Uniqueness and mixing properties of Gibbs measures,
CWI Quarterly 9, 19-24 (1996) . Link

A new lower bound for the critical probability of site percolation on the square lattice,
(with A. Ermakov),
Random Structures and Algorithms 8, 199--212 (1996). Link to article

A note on disjoint-occurrence inequalities for marked Poisson point processes,
J. Appl. Probab. 33, 420-426 (1996). Link to article

A triangle inequality for covariances of binary FKG random variables,
(with A. Gandolfi),
Ann. Appl. Probab. 5, 322-326 (1995). Link to article

Computing Boolean Functions on Anonymous Networks,
(with E. Kranakis and D. Krizanc),
Information and Computation 114, 214-236 (1994).

Disagreement percolation in the study of Markov fields,
(with C. Maes),
Ann. Probab. 22, 749-763 (1994). Link to article

Percolation and the hard-core lattice gas model,
(with J.E. Steif),
Stoch. Proc. Appl. 49, 179-197 (1994). Link to article

A uniqueness condition for Gibbs measures, with application to the 2-dimensional Ising anti-ferromagnet,
Comm.Math.Phys. 152, 161-166 (1993). Link to article

Inequalities for the time constant in first-passage percolation,
(with H. Kesten),
Ann. Appl. Probab. 3, 56-80 (1993). Link to article

Properties of the miss ratio for a 2-level storage model with LRU or FIFO replacement strategy and independent references,
(with D. Towsley),
IEEE Trans. on Comp. 42, 508-512, 1993.

LRU is better than FIFO under the Independent Reference Model,
(with A. Gandolfi),
J. Appl. Probab. 29, 239-243 (1992). Link to article

Stability properties of a flow process in graphs,
(with R.W.J. Meester),
Random Structures and Algorithms 2, 335-341 (1991).

On a Combinatorial Conjecture concerning Disjoint Occurrences of Events,
(with U. Fiebig),
Ann. Probab. 15, 354-374 (1987). Link to article

Disjoint Occurrences of Events: Results and Conjectures,
in: Particle Systems, Random Media and Large Deviations, Contemp. Math. 41, 357-361 (1985).

Inequalities with Applications to Percolation and Reliability,
(with H. Kesten),
J. Appl. Probab. 22, 556-569 (1985). Link to article

Disproof of the Conjectured Subexponentiality of certain Functions in Percolation Theory,
Adv. Appl. Probab. 16, 690-691 (1984).

On the Continuity of the Percolation Probability Function,
(with M. Keane),
in: Conference on Modern Analysis and Probability, Contemp. Math. 26, 61-65 (1984).

A Counterexample to a Conjecture of J.M. Hammersley and D.J.A. Welsh concerning First-Passage Percolation,