Baryshnikov, Y., Melczer, S. and Pemantle, R. (2024).
Asymptotics of multivariate sequences IV: generating functions with poles on a hyperplane arrangement.
Annals of Combinatorics, vol. 28, pages 169--221.
    Published online 13 June, 2023,
DOI 10.1007/s00026-023-00654-2.
Fahrang-Sardroodi, S., Komarova, N., Michelen, M. and Pemantle, R. (2021).
Success probability for selectively neutral invading species in the line model.
Studies in Applied Mathematics, vol. 146, no. 4, pages 1023-1049.
Baryshnikov, Y., Brady, W., Bressler, A. and Pemantle, R. (2010).
Two-dimensional quantum random walk. J. Stat. Phys. vol. 142, pages
78--107.
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Pemantle, R. and Wilson, M. (2010).
Asymptotic expansions of oscillatory integrals with complex phase.
In: Algorithmic Probability and Combinatorics, AMS Contemporary
Mathematics series, vol. 520, pages 221--240.
 
Erratum: in Theorem 4.1 the d/2 in the exponent of the asymptotic series
should have a negative sign in front of it.
Pemantle, R. and Peres, Y. (2010). The critical Ising model on trees,
concave recursions and nonlinear capacity. Ann. Probab. vol. 38,
pages 184-206.
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Pemantle, R. (2010).
Analytic combinatorics in d variables: an overview.
In: Algorithmic Probability and Combinatorics, AMS Contemporary
Mathematics series, vol. 520, pages 195--220.
Pemantle, R. and Wilf, H. (2009).
Counting nondecreasing integer sequences lying below a barrier.
Elec. J. Comb., vol. 16, no. 1, research paper no. 1.
Argiento, R., Pemantle, R., Skyrms, B. and Volkov, S. (2009).
Learning to signal: analysis of a micro-level reinforcement model.
Stoch. Proc. Appl., vo. 119, pages 373-390.
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Pemantle, R. and Wilson, M. (2008). Twenty combinatorial examples of
asymptotics derived from multivariate generating functions. SIAM Review,
vol. 50, pages 199-272.         A directory of
worksheets that accompany the paper
Balogh, J. and Pemantle, R. (2007). The Klee-Minty random edge chain
moves with linear speed. Random Structures and Algorithms, web-published
September, 2006.
click here for ->
PostScript version
Pemantle, R. and Schneider, C. (2007). When is 0.999... equal to 1?
American Mathematical Monthly, volume 114, April issue.
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PostScript version
Pemantle, R. and Peres, Y. (2007). What is the probability of intersecting
the set of Brownian double points?
Annals of Probability, vol. 35 no. 6, pages 2044-2062.
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PostScript version (not as recent as pdf version)
Pemantle, R. (2007). A survey of random processes with reinforcement.
Probability Surveys, volume 4, pages 1-79.
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PostScript version
Corteel, S., Louchard, G. and Pemantle, R. (2006).
Common intervals in permutations.
Discrete Mathematics and Theoretical Computer Science, vol. 8,
pages 189-214.
(Extended abstract, 11 pages).
Pemantle, R. (2005). A probabilistic model for the degree of
the cancellation polynomial in Gosper's Algorithm. J. Algorithms,
vol. 54, pages 58--71.
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Pemantle, R. (2005). Cycles in k-ary random maps and poor performance of
random random number generators. J. Algorithms, vol. 54, pages 72-84.
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Hitczenko, P. and Pemantle, R. (2005). Central Limit Theorem for the Size
of the Range of a Renewal Process. Stat. and Prob. Letters. vol. 72,
pages 249-264.
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Limic, V. and Pemantle, R. (2004). More rigorous results on the
Kauffman-Levin model of evolution. Ann. Probab., vol. 32, pages 2149-2178.
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Pemantle, R. and Wilson, M. (2004). Asymptotics of multivariate sequences,
part II: multiple points of the singular variety. Combinatorics, Probability
and Computing, vol. 13, no. 4., pages 735-761.
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PostScript version
Kakade, S., Kearns, M., Ortiz, L., Pemantle, R. and Suri, S. (2004).
The economics of social networks. In: Proceedings of NIPS, 2004.
Extended abstract, 11 pages.
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PostScript version
Pemantle, R. and Skyrms, B. (2003). Time to absorption in discounted
reinforcement models. Stoch. Proc. Appl., 109, 1-12.
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PostScript version
Pemantle, R. and Skyrms, B. (2003). Network formation by reinforcement
learning: the long and medium run. Math. Soc. Sci, to appear.
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Cohn, H., Pemantle, R. and Propp, J. (2002).
Generating a random sink-free orientation in quadratic time.
Elec. J. Comb., vol. 9, issue 1, paper R10.
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PostScript version
Pemantle, R. and Wilson, M. (2002). Asymptotics of multivariate sequences,
part I: smooth points of the singular variety. J. Comb. Theory, Series A,
vol. 97, 129-161.
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PostScript version
< > erratum
Levin, D., Pemantle, R. and Peres, Y. (2001). A phase transition in
random coin tossing. Ann. Probab. vol. 29, 1637-1669.
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PostScript version
Pemantle, R. (2000). Toward a theory of negative dependence.
J. Math. Phys., 41, 1371 - 1390.
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Haggstrom, O. and Pemantle, R. (2000). Absence of mutual unbounded growth
for almost all parameter values in the two-type Richardson model.
Stoch. Pro. Appl., 90, 207 - 222.
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PostScript version
Pemantle, R. and Peres, Y. (2000). Non-amenable products are not
treeable. Israel J. Math, 118, 147-155.
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PostScript version
Pemantle, R. (2000). Generating functions with high-order poles are
nearly polynomial. In: Mathematics and Computer Science:
Algorithms, trees, combinatorics and probabilities. Birkhauser: Basel.
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PostScript version
Pemantle, R., Peres, Y., Pitman, J. and Yor, M. (2000). Where did the
Brownian particle go? Elec. J. Prob vol. 6, paper 10, 22 pages.
click here for ->
PostScript version
Khoshnevisan, D. and Pemantle, R. (2000). Sojourn times for Brownian sheet.
Period. Math. Hungar. vol. 41, 187-194.
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PostScript version
Haggstrom, O. and Pemantle, R. (1999). On near-critical and
dynamical percolation in the tree case. Rand. Struct. Alg., 15, 311 - 318.
click here for ->
PostScript version
Pemantle, R. and Volkov, S. (1999). Vertex-reinforced random walk on
Z has finite range. Ann. Probab., 27, 1368 - 1388.
Errata: (1) The hypothesis that |J| = 5 is missing from Lemma 4.2;
(2) Lemma 3.3 requires fixing: click here
Pemantle, R. and Steif, J. (1999). Robust Phase Transitions for
Heisenberg and Other Models on General Trees.
Ann. Probab., 27, 876 - 912.
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PostScript version
Pemantle, R. and Rosenthal, J. (1999). Moment conditions for a sequence
with negative drift to be uniformly bounded in L^r. Stoch. Proc. Appl.,
82, 143 - 155.
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PostScript version
Pemantle, R. and Volkov, S. (1998). Markov chains in a field of traps.
J. Theor. Prob., 11, 561 - 569.
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PostScript version
Haggstrom, O. and Pemantle, R. (1998). First passage percolation and a
model for competing spatial growth. J. Appl. Prob., 35, 683 - 692.
click here for ->
PostScript version
Adelman, O., Burdzy, K. and Pemantle, R. (1998). Sets avoided
by Brownian motion. Ann. Prob., 26, 429 - 464.
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PostScript version
Benjamini, I., Pemantle, R. and Peres, Y. (1998). Unpredictable paths
and percolation. Ann. Probab., 26,
1198 - 1211.
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PostScript version
Lyons, R., Pemantle, R. and Peres, Y. (1998). Resistance bounds for
first-passage percolation and maximum flow. J. Comb. Th., ser A, 86,
158 - 168.
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PostScript version
Barlow, M., Pemantle, R. and Perkins, E. (1997). Diffusion
limited aggregation on a homogeneous tree. Prob. Th. Rel. Fields,
107, 1 - 60.
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PostScript version
Pemantle, R. (1997). Sharpness of second moment criteria for branching
and tree-indexed processes. In: Classical and modern
branching processes,, 257 - 262, IMA Vol. Math. Appl.,
84,. Springer: New York.
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PostScript version
Lyons, R., Pemantle, R. and Peres, Y. (1997). Unsolved problems
concerning random walks on trees. In: Classical and modern
branching processes, 223 - 237, IMA Vol. Math. Appl., 84,.
Springer: New York. (Corrected version)
Click here for -> errata sheet
Chayes, L., Pemantle, R. and Peres, Y. (1997). No directed fractal
percolation in zero area. J. Stat. Phys., 88, 1353 - 1362.
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PostScript version
Pemantle, R. (1996). The probability that Brownian motion almost covers
a line. Ann. IHP, Prob. and Stat., 33, 147 - 165.
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PostScript version
Pemantle, R. (1996). Maximum variation of total risk. Stat. Prob.
Letters, 28, pages 285 - 289.
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PostScript version
Benjamini, I., Pemantle, R. and Peres, Y. (1996). Random walks in varying
dimensions. J. Theor. Prob., 9, 231 - 244.
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PostScript version
Lyons, R., Pemantle, R. and Peres, Y. (1996). Random walks on the
Lamplighter group. Ann. Probab., 24, 1993 - 2006.
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PostScript version
Pemantle, R., Peres, Y. and Shapiro, J. (1996). The trace of spatial
Brownian motion is capacity-equivalent to the unit square. P.T.R.F.,
106, 379 - 399.
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PostScript version
Lyons, R., Pemantle, R. and Peres, Y. (1996). Biased random walks on
Galton-Watson trees. P.T.R.F., 106, 249 - 264.
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PostScript version
Pemantle, R. and Peres, Y. (1995). Critical RWRE on trees
and tree-indexed random walks. Ann. Probab., 23, 105 - 140.
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PostScript version
Pemantle, R. and Peres, Y. (1995). Galton-Watson trees
with the same mean have the same polar sets. Ann. Probab., 23,
1102 - 1124.
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PostScript version
Benjamini, I., Pemantle, R. and Peres, Y. (1995). Martin capacity for
Markov chains. Ann. Probab., 23, 1332 - 1346.
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PostScript version
Lyons, R., Pemantle, R. and Peres, Y. (1995). A conceptual
proof of the Kesten-Stigum theorem. Ann. Probab., 23, 1125 - 1138.
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PostScript version
Pemantle, R. (1995). Tree-indexed processes. Stat. Sci., 5,
200 - 213.
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PostScript version
Pemantle, R. and Peres, Y. (1994). Domination between trees
and application to an explosion problem. Ann. Probab., 22,
180 - 194.
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Pemantle, R. and Peres, Y. (1994). Planar first-passage times
are not tight. In: Probability and Phase Transition, G. Grimmett Editor,
261 - 264. Kluwer: Boston. http://www.wkap.nl/prod/b/0-7923-2720-9
click here for ->
Published version in PostScript
Pemantle, R. (1994). A shuffle that mixes sets of any fixed
size much faster than it mixes the whole deck. Rand. Struct. Alg.,
9, 609 - 625.
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PostScript version
Burton, R. and Pemantle, R. (1993). Local characteristics,
entropy and limit theorems for uniform spanning trees and domino tilings
via transfer-impedances. Ann. Prob., 21, 1329 - 1371.
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PostScript version
Pemantle, R. (1993). Critical RWRE on trees of exponential
growth. Proc. Sem. Stoch. Pro. 1992, Burdzy and Bass, editors,,
221 - 240.
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PostScript version
Fill, J. and Pemantle, R. (1993). Oriented percolation,
first-passage percolation and covering times for Richardson's
model on the n-cube. Ann. Appl. Prob., 3, 593 - 629.
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PostScript version
Pemantle, R. (1992). Automorphism-invariant measures
on trees. Ann. Probab., 20, 1549 - 1566.
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PostScript version
Pemantle, R. (1992). The contact process on trees. Ann.
Probab., 20, 2089 - 2116.
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PostScript version
Pemantle, R. and Penrose, M. (1992). On path integrals for the
high-dimensional Brownian bridge. J. Comput. Appl. Math.,
44, 381 - 390.
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PostScript version
Pemantle, R. (1991). Choosing a spanning tree for the
integer lattice uniformly. Ann. Probab., 19, 1559 - 1574.
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PostScript version
Pemantle, R. (1990).
A time-dependent version of Polya's urn. Jour. Theor. Prob.,
3, 627 - 637.
Pemantle, R. (1990). Vertex-reinforced random walk. Prob.
Theor. and Rel. Fields, 92, 117 - 136.
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PostScript version
Pemantle, R. (1989). Randomization time for the overhand shuffle.
J. Theor. Prob., 2, 37 - 49.
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PostScript version
Pemantle, R. (1994). Uniform random spanning trees. In: Topics
in contemporary probability and its applications, J. L. Snell, editor,
pages 1 - 54. CRC Press: Boca Raton.
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PostScript version
Dissertations
Mine
Pemantle, R. (1988).
Random Processes with Reinforcement.
Ph.D. Thesis, Department of Mathematics, Massachusetts Institute
of Technology.
Ph.D. Students
Jin, Kaitian (2024).
Coefficient asymptotics of multivariable algebraic power series and
rational power series with pseudo multiple points.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Goodman, Eric (2022).
Counting extreme points from Poisson processes on a half line.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Gillen, Stephen (2022).
Geometry of gradient flows for analytic combinatorics.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Xia, Jiaming (2022).
Asymptotic properties of disordered systems.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Michelen, Marcus (2019).
Percolation on Galton-Watson trees.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Rosenberg, Josh (2018).
Sharp thesholds for the frog model and related systems.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Chen, Albert (2018).
Opinion Broadcasting Model.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Greenwood, Torin (2015).
Asymptotics of bivariate generating functions with algebraic singularities.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Poh, Julius (2015).
Shape and other properties of 1324-avoiding permutations.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Subramanian, Sneha (2014).
Zeros, critical points and coefficients of random functions.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Ding, Shanshan (2014).
A random walk in representations.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Abuzzahab, Omar (2013).
The 2-core of a Random Inhomogeneous Hypergraph.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Kariv, Jonathan (2013).
Broken Telephone, an analysis of a reinforced process.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
DeVries, Tim (2011).
Algorithms for bivariate singularity analysis.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Lugo, Michael (2010).
Profiles of large combinatorial structures.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Bressler, Andrew (2009).
Quantum Random Walks on the Integer Lattice Via Generating Functions.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Zhu, Tong (2009).
Nonlinear Polya Urn Models and Self-Organizing Processes.
Ph.D. Thesis, Department of Mathematics, University of Pennsylvania.
Lladser, Manuel (2003).
Asymptotic Enumeration via Singularity Analysis.
Ph.D. Thesis, Department of Mathematics, Ohio State University.
Masters Students
Zhou, Weichen (2021).
Advantage of mutants in a stochastically selectively neutral environment.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Son, Jaesung (2018).
Mean-field theory of spin glasses and Boolean satisfiability.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Pham, Phil (2016).
Just how easy is it to cheat a linear regression?
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Cao, Chang (2015).
Stochastic process and Girsanov theory.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Jiao, Kevin (2014).
The range of two dimensional simple random walk.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Choi, Brian (2012).
Proof of the Hartman-Wintner Law of the Iterated Logarithm.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Du, Peter (2011).
The Aztec diamond edge-probability generating function.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Brady, William (2007).
Quantum Random Walks on Z^2.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Dicker, Lee (2006).
Coloring a d >= 3 dimensional lattice with two independent random walks.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
Utgoff, Naomi (2005).
Credible Signalling in the "Letters of Recommendation" Game.
Masters Thesis, Department of Mathematics, University of Pennsylvania.
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