Ross Pinsky's Home Page

I am a professor in the Department of Mathematics at the Technion -Israel Institute of Technology.

B.A.    University of Pennsylvania, 1978
Ph.D    New York University - Courant Institute of Mathematical Sciences, 1982 under the direction of S.R.S. Varadhan.

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

Haifa, 32000

Technion Probability Web Site


Advanced Probability---Fall 2016

Number Theory—Spring 2014


**New Book**

Problems from the Discrete to the Continuous

Probability, Number Theory, Graph Theory, and Combinatorics, Springer 2014


(Above picture from "Mathematics at the Bar" talk, May 9, 2016 .)

My book, Positive 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. 


The speed of a general random walk reinforced by its recent history, (pdf)

Some connections between permutation cycles and Touchard polynomials and between permutations that fix a set and covers of multisets, (pdf),  Electron. Commun. Probab. 22 (2017), Paper No. 17, 9 pp.

On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables, (pdf)

A natural probabilistic model on the integers and its relation to Dickman-type distributions and Buchstab's function, (pdf)

Transience, recurrence and the speed of a random walk in a site-based feedback environment, (with Nick Travers) (pdf), Probab. Theory Related Fields 167 (2017),  917–978.

Transience/recurrence and growth rates for diffusion processes in time-dependent regions, (pdf), Electronic J.  Probab. (2016), 24 pp.

The behavior of the  free boundary for  reaction-diffusion equations with convection in an exterior domain with Neumann or Dirichlet boundary condition (pdf), J. Differential Equations, 260 (2016),  5075-5102.

Universal bound independent of geometry for solution to symmetric diffusion equation in exterior domain with boundary flux (pdf), preprint

The speed of a random walk excited by its recent history (pdf) Adv. in Appl. Probab. 48, (2016), 215-234.

Probabilistic and combinatorial aspects of the card-cyclic to random shuffle (pdf) ,  Random Structures and Algorithms, 46, (2015), 362-390.

Transience, recurrence and speed of diffusions with a non-Markovian two-phase ``use it or lose it'' drift (pdf),   Annales l'Institut Henri Poincare, 50, (2014), 1198-1212.

Cyclic to random transposition shuffles (pdf), preprint

Detecting tampering in a random hypercube (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.

A probabilistic approach to bounded/positive solutions for Schrodinger operators with certain
classes of potentials
(pdf), Trans. Amer. Math. Soc., 360 (2008) no. 12, 6545-6554.

Regularity properties of the Donsker-Varadhan rate functional
for non-reversible diffusions and random evolutions
(pdf), Stochastics and Dynamics, 7 (2007) no. 2, 123-140.

Spectral 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.

Positive solutions of reaction diffusion equations with super-linear absorption:
universal bounds, uniqueness for the Cauchy problem, boundedness
of stationary solutions
(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.

On 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).

Comparison 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.

Spectral gap and rate of convergence to equilibrium for a class of conditioned Brownian motions (pdf),
Stoch. Processes and Their Applications, 115 (2005), no. 6, 875-889.

Absolute 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.

The 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.

Strong 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.

Asymptotics 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.

Finite 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.

The behavior of the life span  for solutions to u_t=\Delta u+a(x)u^p in R^d (pdf) 
J. Differential Equations 147 (1998), no. 1, 30--57.