Ross Pinsky's Home Page
(Above picture from "Mathematics at the Bar" talk, May 9, 2016 .)
My mathematical interests are in Probability and Stochastic Processes and in Linear and Nonlinear Parabolic and Elliptic Partial Differential Equations.
Address: Department of Mathematics
Technion-Israel Institute of Technology
Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and Combinatorics Universitext, Springer 2014
Harmonic Functions and Diffusion
is available from
Cambridge University Press in hardback, paperback and e-book form.
Below are my papers since 1998. (Here's a link to all my papers at MathSciNet.)
© All material accessible through this page is copyrighted by Ross Pinsky and his coauthors and by the corresponding publishers. Permission is granted for fair use in personal, noncommercial, and academic projects.
A Modest Proposal: In order that the author may accrue some benefit from the burgeoning funds rapidly becoming available in the field of nanotechnology, the reader is kindly requested to treat all small, positive epsilons appearing in the articles below as being smaller than 10 to the minus 9th power.
and Analysis in Interacting Physical Systems - in Honor of
S.R.S. Varadhan, Springer (2019), 267-294.
, Random Structures and Algorithms, 46, (2015), 362-390.(pdf)
Annales l'Institut Henri Poincare, 50, (2014), 1198-1212.(pdf),
(pdf), Electronic J. Probab., 18, (2013), 1-12
Asymptotics for exit problem and principal eigenvalue for a class of non-local elliptic operators related to diffusion processes with random jumps and vanishing diffusion (pdf), Bull. Inst. Math. Academia Sinica N.S., 7 (2012), no. 1, 545-564.
Asymptotic behavior of the principal eigenvalue for a class of non-local elliptic operators related to Brownian motion with spatially dependent random jumps, (with N. Arcusin) (pdf), Communications Contemp. Math., 13 (2011), no. 6, 1077-1093.
A probabilistic approach to the Liouville property for Schr\"odinger operators with an application to infinite configurations of balls (with R. Hess-Green) (pdf), Proc. Amer. Math. Soc., 138 (2010), no. 12, 4487-4496.
One-dimensional diffusions that eventually stop down-crossing (pdf), Bull. London Math. Soc., 42 (2010), no. 4, 634-638.
Transience/recurrence and the speed of a one-dimensional random walk in a ``have your cookie and eat it'' environment (pdf), Annales de l'Institut Henri Poincare, Probabilites et Statistiques, 46 (2010), no. 4, 949-964.
Explicit and almost explicit spectral calculations for diffusion operators (pdf), J. Funct. Anal., 256 (2009) no. 10, 3279-3312.
Transience/recurrence for normally reflected Brownian motion in unbounded domains (pdf), Ann. Probab. 37 (2009) no. 2, 676-686.
Spectral analysis of a class of non-local elliptic operators related to Brownian motion with random jumps (pdf), Trans. Amer. Math. Soc., 361 (2009) no. 9, 5041-5060.
Ergodic behavior of diffusions with random jumps from the boundary (with I. Ben Ari) (ps), Stoch. Processes and Their Applications, 119 (2009) no. 3, 864-881.
The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain (pdf), J. Differential Equations, 246 (2009) no. 6, 2561-2576.
probabilistic approach to bounded/positive solutions for Schrodinger operators
classes of potentials (pdf), Trans. Amer. Math. Soc., 360 (2008) no. 12, 6545-6554.
properties of the Donsker-Varadhan rate functional
for non-reversible diffusions and random evolutions (pdf), Stochastics and Dynamics, 7 (2007) no. 2, 123-140.
analysis of a family of second-order elliptic operators with nonlocal boundary
condition indexed by
a probability measure (with I. Ben Ari) (pdf), J. Funct. Anal., 251 (2007) no. 1, 122-140.
When the law of large numbers fails for increasing subsequences of random permutations (pdf), Ann. Probab. 35 (2007) no. 2, 758-772.
The compact support property for measure-valued processes (with J. Englander) (pdf), Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques, 42 (2006) no. 5, 535-552.
(pdf), J. Differential Equations, 220 (2006), no. 2, 407-433.
Law of large numbers for increasing subsequences of random permutations (pdf), Random Structures and Algorithms, 29, (2006) no. 3, 277-295.
domain monotonicity for the principal eigenvalue of the Laplacian
with a mixed Dirichlet-Neumann boundary condition (pdf), Geometry, spectral theory, groups, and dynamics, 245--252,
Contemp. Math., 387, Amer. Math. Soc., Providence, R.I. (2005).
theorems for the spectral gap of diffusions processes
and Schr\"odinger operators on an interval (pdf), J. London Math. Soc., 72 (2005), no. 3, 621-631.
Global existence/nonexistence for sign-changing solutions
to $u_t=\Delta u+|u|^p$ in $R^d$ (pdf), Bull. London Math.l Soc., 37 (2005), no. 3, 417-426.
gap and rate of convergence to equilibrium for a class of conditioned Brownian
Stoch. Processes and Their Applications, 115 (2005), no. 6, 875-889.
continuity/singularity and relative entropy properties for probability measures
induced by diffusions
on infinite time intervals (with I. Ben Ari) (pdf), Stoch. Processes and Their Applications, 115 (2005), no. 2, 179-206.
shift of the principal eigenvalue for the Neumann Laplacian in a domain with many
small holes in R^d, d\ge2 (pdf),
Asymptotics of the principal eigenvalue and expected hitting time for positive recurrent elliptic operators
in a domain with a small puncture (pdf) J. Func. Anal., 200 (2003), no. 1, 177-197.
Uniqueness/nonuniqueness for nonnegative solutions of second order parabolic equations of the form u_t=Lu+Vu-\gamma u^p in R^n (with J. Englander) (pdf), J. Differential Equations, 192 (2003), no. 2, 396-428.
law of large numbers and mixing for the invariant distributions of
measure-valued diffusions (pdf), Stoch. Processes and Their Applications, 105 (2003), no. 1, 117-137.
for the heat equation in the exterior of a shrinking compact set in the
plane via Brownian hitting times (pdf), Proc. Amer. Math. Soc. 130 (2002), no. 6, 1673--1679.
Invariant Probability Distributions for Measure-Valued Diffusions (pdf), Ann. Probab. 29 (2001), no. 4, 1476--1514.
Decay of mass for the equation u_t=\Delta u-a(x)u^p|\nabla u|^q (pdf), J. Differential Equations 165 (2000), no. 1, 1--23.
A probabilistic approach to positive harmonic functions in a slab
with alternating Dirichlet and Neumann boundary conditions, Trans. Amer. Math. Soc. 352 (2000), no. 6, 2445--2477.
Time Blow-up for the inhomogeneous equation
u_t=\Delta u+a(x)u^p+\lambda\phi in R^d (pdf), Proc. Amer. Math. Soc.
127 (1999), no. 11, 3319--3327.
On the construction
and support properties of measure-valued diffusions on $D\subseteqR\sp d$ with
spatially dependent branching (with J. Englander) (pdf) Ann. Probab. 27
(1999), no. 2, 684--730.
behavior of the life span for solutions to u_t=\Delta u+a(x)u^p in R^d
J. Differential Equations 147 (1998), no. 1, 30--57.