Asaf Nachmias
Professor
Department of Mathematical Sciences
Tel Aviv University
Tel Aviv 6997801
Israel
email:
asafnach @ tauex (dot) tau (dot) ac (dot) (obvious)
Research interests:
Probability theory and statistical physics.
Saint Flour lecture notes
Planar maps, random walks and circle packing
.
Binge
the lectures.
Papers
The local limit of uniform spanning trees
(with
Yuval Peres
),
Probability Theory and Related Fields
,
to appear
.
The diameter of the uniform spanning tree of dense graphs
(with
Noga Alon
and
Matan Shalev
),
submitted
.
The diameter of uniform spanning trees in high dimensions
(with
Peleg Michaeli
and
Matan Shalev
),
Probability Theory and Related Fields
, 179, 261-–294 (2021).
The Dirichlet problem for orthodiagonal maps
(with
Ori Gurel-Gurevich
and
Daniel Jerison
),
Advances in Mathematics
, 374, (2020).
A combinatorial criterion for macroscopic circles in planar triangulations
(with
Ori Gurel-Gurevich
and
Daniel Jerison
),
submitted
.
The local limit of the uniform spanning tree on dense graphs
(with
Jan Hladky
and
Tuan Tran
),
Journal of Statistical Physics
,
Volume 173, Issue 3-4, pp 502-545
, special issue devoted to Complex Networks.
Geometric and spectral properties of causal maps
(with
Tom Hutchcroft
and
Nicolas Curien
),
Journal of the European Mathematical Society (JEMS)
, 22 no. 12, 3997–-4024 (2020).
Hyperbolic and Parabolic Unimodular Random Maps
(with
Omer Angel
,
Tom Hutchcroft
,
Gourab Ray
),
Geometric and Functional Analysis (GAFA)
,
28, 879-942, 2018
.
Slightly subcritical hypercube percolation
(with
Tim Hulshof
),
Random Structures and Algorithms
, 56 no. 2, 557--593 (2020).
Uniform Spanning Forests of Planar Graphs
(with
Tom Hutchcroft
),
Forum of Mathematics, Sigma
, 7, E29 (2019).
Indistinguishability of Trees in Uniform Spanning Forests
(with
Tom Hutchcroft
),
Probability Theory and Related Fields
,
Volume 168, Issue 1-2, pp 113-152, 2017.
Recurrence of multiply-ended planar triangulations
(with
Ori Gurel-Gurevich
and
Juan Souto
),
Electronic Communications in Probability
,
Volume 22, no. 5, 1-6, 2017
.
Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk
, (with
Omer Angel
,
Tom Hutchcroft
,
Gourab Ray
),
Inventiones Mathematicae
,
206, 229-268, 2016
.
Random walks on stochastic hyperbolic half planar triangulations
(with
Omer Angel
,
Gourab Ray
),
Random Structures and Algorithms
,
49 (2), 213--234, 2016
.
Boundaries of planar graphs, via circle packings
(with
Omer Angel
,
Martin Barlow
,
Ori Gurel-Gurevich
),
Annals of Probability
,
44 no.3, 1956--1984, 2016
.
Electrical resistance of the low dimensional critical branching random walk
(with
Antal Jarai
),
Communications in Mathematical Physics
,
331, 67-109, 2014
.
Unlacing the lace expansion: a survey to hypercube percolation
(with
Remco van der Hofstad
),
Metrika
,
77 no. 1, 23-50, 2014
.
Rate of Convergence for Cardy's Formula
(with
Dana Mendelson
and
Sam Watson
),
Communications in Mathematical Physics
,
329, 29-56, 2014.
Non-amenable Cayley graphs of high girth have p_c < p_u and mean-field exponents
(with
Yuval Peres
),
Electronic Communications in Probability
,
17, no. 57, 1--8, 2012.
Recurrence of planar graph limits
(with
Ori Gurel-Gurevich
),
Annals of Mathematics
,
177 no. 2, 761-781, 2013.
Hypercube Percolation
(with
Remco van der Hofstad
),
Journal of the European Mathematical Society (JEMS)
,
Volume 19, Issue 3, pp. 725-814, 2017.
A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics
(with Yun Long, Weiyang Ning and
Yuval Peres
)
Memoirs of the AMS
,
232, no. 1092, 2014.
Non-concentration of return times
(with
Ori Gurel-Gurevich
),
Annals of Probability
,
41, no. 2, 848-870, 2013.
The evolution of the cover time
(with
Martin Barlow
,
Jian Ding
and
Yuval Peres
),
Combinatorics, Probability and Computing
,
20, 331-345, 2011.
Arm exponents in high dimensional percolation
(with
Gady Kozma
),
Journal of the American Mathematical Society (JAMS)
,
24, 375-409, 2011.
A note about critical percolation on finite graphs
(with
Gady Kozma
),
Journal of Theoretical Probability
,
24, no. 4, 1087-1096, 2011.
Is the critical percolation probability local?
(with
Itai Benjamini
and
Yuval Peres
),
Probability Theory and Related Fields
,
149, no. 1-2, 261-269, 2011.
The Alexander-Orbach conjecture holds in high dimensions
(with
Gady Kozma
),
Inventiones Mathematicae
,
178, no. 3, 635--654, 2009.
Testing the expansion of a graph
(with
Asaf Shapira
),
Information and Computation
,
208, no. 4, 309-314, 2010.
Mean-field conditions for percolation on finite graphs
,
Geometric and Functional Analysis (GAFA)
,
19, 1171-1194, 2009.
Mixing time power laws at criticality
, (with Yun Long and
Yuval Peres
),
Proc. of the 48th IEEE FOCS
,
2007.
Critical percolation on random regular graphs
, (with
Yuval Peres
),
Random Structures and Algorithms
,
36, no. 2, 111-148, 2010.
Critical random graphs: diameter and mixing time
, (with
Yuval Peres
),
Annals of Probability
,
36, no. 4, 1267-1286, 2008.
Component sizes of the random graph outside the scaling window
, (with
Yuval Peres
),
Latin American Journal of Probability and Mathematical Statistics (ALEA)
,
3, 133-142, 2007.
The critical random graph, with martingales
, (with
Yuval Peres
),
Israel Journal of Math
,
176, 29-43, 2010.
Colouring complete bipartite graphs from random lists
, (with
Michael Krivelevich
),
Random Structures and Algorithms
29, no. 4, 436-449, 2006.
Colouring powers of cycles from random lists
, (with
Michael Krivelevich
),
European Journal of Combinatorics
,
25, 961-968, 2004.
Editorial work
Annales de l'Institut Henri Poincaré (B)
, associate editor, 2016---present.
Annals of Probability
, associate editor, 2021---present.
Some online lectures
48th Saint Flour lectures (8 lectures, 1.5 hours each)
The local limit of uniform spanning trees
Recurrence of planar graph limits
Hypercube percolation
Critical percolation on finite graphs
The diameter and mixing time of critical random graphs
Teaching
Brownian Motion
, Spring 2021.
Complex analysis 2
, Tel Aviv university, Spring 2019.
Planar maps, random walks and the circle packing theorem
, Tel Aviv university, Fall 2017.
Probability in 2D
, Tel Aviv university, Fall 2016.
Graduate seminar in discrete probability
, Tel-Aviv university, Fall 2015.
Random spanning trees
in Tel-Aviv university, Fall 2014.
Random walks on random fractals
,
PIMS summer school in probability
, 2014.
Math 321
, Real Variables II, January 2014.
Math 548
, Discrete probability, January 2014.
Math 220
, Mathematical Proof, September 2013.
Math 608
, Topics in probability: 2D statistical physics, January 2013.
Math 302
, Introduction to probability, January 2013.
Organization
Random networks
, Oberwolfach, 2013.
Recent trends in stochastic analysis
, UBC, 2013.
Probability on Trees and Planar Graphs
, Banff, 2014.
PIMS summer school in probability
, UBC, 2014.
Elegance in probability
, a conference honoring Russell Lyons's 60th birthday, Tel Aviv, 2017.
Figures from research