**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 po wer.

Two measures of efficiency for the secretary problem with multiple items at each rank

The secretary problem with biased arrival order via a Mallows distribution, Adv. in App. Math. 140 (2022), Paper No. 102386, 9 pp.

Clustering of consecutive numbers in permutations avoiding a pattern and in separable permutations

Large time probability of failure in diffusive search with resetting for a random target in $\mathbb{R}^d$–a functional analytic approachlargetime**, **to appear in Trans. Amer. Math. Soc.

**Clustering of consecutive numbers under Mallows distributions and super clustering under general p-shifted distributions,** Electron. J. Probab. 27 (2022), 20 pp.

**Comparing the inversion statistic for distribution-biased and distribution-shifted ****permutations with the geometric and the GEM distributions, ** ALEA-Lat. Am. J. Probab. Math. Stat., 19, (2022), 209-229.

**A view from the bridge spanning combinatorics and probability, **Enumerative Combinatorics and Applications, 1 (2021), article s2s3.

**The infinite limit of separable permutations,** Random Structures Algorithms, 59 (2021), 622-639.

**Permutations avoiding a certain pattern of length three under Mallows distributions, **Random Structures Algorithms, 58 (2021), 676-690.

**An identity involving Stirling numbers of both kinds and its connection to right-to-left minima of certain set partitions** (with Orli Herscovici), manuscript

**Probabilistic proofs of some generalized Mertens’ formulas via generalized Dickman distributions, **manuscript

**The speed of a general random walk reinforced by its recent history, **Stochastic Process. Appl. 130 (2020), 4793-4807.

**The infinite limit of random permutations avoiding patterns of length three,** Combin. Probab. Comput. 29 (2020), 137-152.

**Diffusive search with spatially dependent resetting, **Stochastic Process. Appl. 130 (2020), 2954-2973 .

**Optimizing the drift in a diffusive search for a random stationary target, **Electron. J. Probab., Paper No.82, (2019) 22 pp.

**Kemeny’s constant for one-dimensional diffusions,** Electron. Commun. Probab. 24 (2019), Paper No. 36, 5 pp.

**A natural probabilistic model on the integers and its relation to Dickman-type distributions and Buchstab’s function, **Probability and Analysis in Interacting Physical Systems – in Honor of S.R.S. Varadhan, Springer (2019), 267-294.

**On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables,** Electron. J. Probab. 23 (2018), Paper No. 3, 17 pp.

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

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

**Transience/recurrence and growth rates for diffusion processes in time-dependent regions, **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,** J. Differential Equations, 260 (2016), 5075-5102.

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

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

**Probabilistic and combinatorial aspects of the card-cyclic to random shuffle, **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,** Annales l’Institut Henri Poincare, 50, (2014), 1198-1212.

**Cyclic to random transposition shuffles, **preprint

**Detecting tampering in a random hypercube, **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, **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) 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), Proc. Amer. Math. Soc., 138 (2010), no. 12, 4487-4496.

**One-dimensional diffusions that eventually stop down-crossing, **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, **Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 46 (2010), no. 4, 949-964.

**Explicit and almost explicit spectral calculations for diffusion operators, **J. Funct. Anal., 256 (2009) no. 10, 3279-3312.

**Transience/recurrence for normally reflected Brownian motion in unbounded domains, **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, **Trans. Amer. Math. Soc., 361 (2009) no. 9, 5041-5060.

**Ergodic behavior of diffusions with random jumps from the boundary** (with I. Ben Ari), 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, **J. Differential Equations, 246 (2009) no. 6, 2561-2576.

**A probabilistic approach to bounded/positive solutions for Schrodinger operators with certain classes of potentials, **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**, 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), J. Funct. Anal., 251 (2007) no. 1, 122-140.

**When the law of large numbers fails for increasing subsequences of random permutations, **Ann. Probab. 35 (2007) no. 2, 758-772.

**The compact support property for measure-valued processes (with J. Englander), **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, **J. Differential Equations, 220 (2006), no. 2, 407-433.

**Law of large numbers for increasing subsequences of random permutations, **Random Structures Algorithms, 29, (2006) no. 3, 277-295.

**On domain monotonicity for the principal eigenvalue of the Laplacian with a mixed Dirichlet-Neumann boundary condition, **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,** 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 $R^d$, **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, **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), 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,** manuscript.

**Asymptotics of the principal eigenvalue and expected hitting time for positive recurrent elliptic operators in a domain with a small puncture, **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), J. Differential Equations, 192 (2003), no. 2, 396-428.

**Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions, **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,** Proc. Amer. Math. Soc. 130 (2002), no. 6, 1673–1679.

**Invariant Probability Distributions for Measure-Valued Diffusions, **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, **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, **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) 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,** J. Differential Equations 147 (1998), no. 1, 30–57.