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**.

Email: Pinsky@math.technion.ac.il

Address: Department of Mathematics

Technion-Israel Institute of Technology

Haifa, 32000

Israel

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*Random Permutations and some Connections to
Probabilistic Number Theory---Fall 2015*

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**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.

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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. __

Transience/Recurrence
and Growth Rates for Diffusion Processes in Time-Dependent Regions, (pdf), Electronic J. Probab. (2016), 24
pp.

Transience,
recurrence and the speed of a random walk in a site-based feedback environment, (with Nick Travers) (pdf),
to appear in Probab. and Related Fields

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.

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),

preprint

__
__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.