---
### Preprints
* R. Raquépas, J. Schenker, "Quenched large deviations of Birkhoff sums along random quantum measurements," 2024. [arXiv:2410.15465](https://arxiv.org/abs/2410.15465)
* J. Kraisler, J. Schenker, J. C. Schotland, "Dynamic One Photon Localization in a Discrete Model of Quantum Optics," 2024. [arXiv:2407.14109](https://arxiv.org/abs/2407.14109)
* O. Ekblad, J. Schenker. "Ergodic repeated interaction quantum systems: Steady states and reducibility theory," 2024. [arXiv:2406.10982](https://arxiv.org/abs/2406.10982)
* O. Ekblad, E. Moreno-Nadales, L. Pathirana, J. Schenker, "Asymptotic Purification of Disordered Quantum Trajectories", 2024. [arXiv:2404.03168](https://arxiv.org/abs/2404.03168)
### Books

*  J. R. Miller, C.G. Adams, P.A. Weston, J. H. Schenker, Trapping of small animals moving randomly: Principles and Applications to Pest Monitoring and Management. [SpringerBriefs in Ecology 2015](http://www.springer.com/life+sciences/ecology/book/978-3-319-12993-8). 116 pages.

### Papers

1. J. H. Schenker, J. W. Swift, “Observing the symmetry of attractors,” [Phys. D 114 (1998), 315–337](http://dx.doi.org/10.1016/S0167-2789(97)00191-7). [arXiv:chao-dyn/9706009](http://arxiv.org/abs/chao-dyn/9706009)
1. M. Aizenman, R. M. Friedrich, D. Hundertmark, J. H. Schenker, “Constructive fractional-moment criteria for localization in random operators,” [Phys. A 279 (2000), 369–377](http://dx.doi.org/10.1016/S0378-4371(00)00012-1). [arXiv:math-ph/0001035](http://arxiv.org/abs/math-ph/0001035)
1. M. Aizenman, J. H. Schenker, “The creation of spectral gaps by graph decoration,” [Lett. Math. Phys. 53 (2000), 253–262](http://link.springer.com/article/10.1023%2FA%3A1011032212489). [arXiv:math-ph/0008013](http://arxiv.org/abs/math-ph/0008013)
1. B. Chen, J. H. Schenker, “Molecular dynamics simulations of gases using a split-Hamiltonian method,” [Appl. Num. Math. 38 (2001), 21-48](http://dx.doi.org/10.1016/S0168-9274(00)00060-X).
1. M. Aizenman, R. M. Friedrich, D. Hundertmark, J. H. Schenker, “Finite-volume fractional moment criteria for Anderson localization,” [Commun. Math. Phys. 224 (2001), 219-254](http://dx.doi.org/10.1007/s002200100441). [arXiv:math-ph/9910022](http://arxiv.org/abs/math-ph/9910022)
1. A. Elgart, J. H. Schenker, “A strong operator topology adiabatic theorem,” [Rev. Math. Phys. 14 (2002), 569- 584](http://dx.doi.org/10.1142/S0129055X02001247). [arXiv:math-ph/0110002](http://arxiv.org/abs/math-ph/0110002)
1. M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, G. Stolz, “Fractional moment methods for Anderson localization in the continuum,” Proceedings of the ICMP (Lisbon 2003), World Scientific. [arXiv:math-ph/0309018](http://arxiv.org/abs/math-ph/0309018)
1. J. H. Schenker, “Hölder equicontinuity of the density of states at weak disorder," [Lett. Math. Phys. 70 (2004), 195-209](http://dx.doi.org/10.1007/s11005-004-3757-x). [arXiv:math-ph/0403063](http://arxiv.org/abs/math-ph/0403063)
1. A. Figotin, J. H. Schenker, “Spectral theory of time dispersive and dissipative systems," [J. Stat. Phys. 118 (2005), 199-263](http://dx.doi.org/10.1007/s10955-004-8783-7). [arXiv:math-ph/0404070](http://arxiv.org/abs/math-ph/0404070)
1. H. Schulz-Baldes, J. H. Schenker, “Semicircle law and freeness for random matrices with symmetries or correlations,” [Math. Res. Lett. 12 (2005), 531-542](http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2005/0012/0004/MRL-2005-0012-0004-a007.pdf). [arXiv:math-ph/0505003](http://arxiv.org/abs/math-ph/0505003)
1. J.-M. Bouclet, F.Germinet, A.Klein, J. Schenker, “Linear response theory for magnetic Schrödinger operators in disordered media,” [J. Func. Anal. 226 (2005), 301-372](http://dx.doi.org/10.1016/j.jfa.2005.02.002). [arXiv:math-ph/0408028](http://arxiv.org/abs/math-ph/0408028)
1. P. D. Hislop, F. Klopp, J. Schenker, “Continuity with respect to disorder of the integrated density of states,” [Illinois. J. of Math. 49 (2005), 893-904](https://projecteuclid.org/download/pdf_1/euclid.ijm/1258138226). [arXiv:math-ph/0409007](http://arxiv.org/abs/math-ph/0409007)
1. A. Elgart, G.-M. Graf, J. H. Schenker, “Equality of edge and bulk Hall conductances in a mobility gap,” [Comm. Math. Phys. 259 (2005), 185-221](http://link.springer.com/article/10.1007%2Fs00220-005-1369-7).  [arXiv:math-ph/0409017](http://arxiv.org/abs/math-ph/0409017)
1. M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, G. Stolz, “Moment analysis for localization in random Schrödinger operators,” [Invent. Math. 163 (2006), 343-413](http://dx.doi.org/10.1007/s00222-005-0463-y). [arXiv:math-ph/0308023](http://arxiv.org/abs/math-ph/0308023) 
1. A. Figotin, J. H. Schenker, “Hamiltonian treatment of time dispersive and dissipative media within the linear response theory,” [J. Comp. Appl. Math. 204 (2007), 199-208](http://dx.doi.org/10.1016/j.cam.2006.01.038). [arXiv:physics/0410127](http://arxiv.org/abs/physics/0410127)
1. A. Figotin, J. H. Schenker,  “Hamiltonian extension and eigenfunctions for a time dispersive dissipative string,” in Probability and Mathematical Physics, Proceeding of the conference celebrating 65th birthday of Stanislav Molchanov (Dawson, Jaksic, and Vainberg, eds.), CRM Proceedings and Lecture Notes, vol. 42, AMS, Providence. [arXiv:math-ph/0604001](http://arxiv.org/abs/math-ph/0604001)
1. H. Schulz-Baldes, J. H. Schenker, “Gaussian fluctuations for random matrices with correlated entries,” [Inter. Math. Res. Not. 2007, Vol. 2007, article ID rmn047, 36 pages](http://imrn.oxfordjournals.org/content/2007/rnm047). [arXiv:math-ph/0607028](http://arxiv.org/abs/math-ph/0607028)
1. A. Figotin, J. H. Schenker, “Hamiltonian structure for dissipative and dispersive dynamical systems,”  [J. Stat. Phys. , 128 (2007), 969-1056](http://dx.doi.org/10.1007/s10955-007-9321-1). [arXiv:math-ph/0608003](http://arxiv.org/abs/math-ph/0608003)
1. F. Germinet, A. Klein, J. H. Schenker, “Dynamical delocalization in random Landau Hamiltonians,” [Ann. of Math., 166 (2007), 215-244](http://annals.math.princeton.edu/2007/166-1/p06). [arXiv:math-ph/0412070](http://arxiv.org/abs/math-ph/0412070)  
1. F. Germinet, A. Klein, J. H. Schenker, “Quantization of the Hall conductance and delocalization in ergodic Landau Hamiltonians,”  [Rev. Math. Phys. 21 (2009), 1045–1080](http://dx.doi.org/10.1142/S0129055X09003815). [arXiv:0812.0392](http://arxiv.org/abs/0812.0392)
1. Y. Kang, J. Schenker, “Diffusion of wave packets in a Markov random potential,” [J. Stat. Phys. 134 (2009), 1005-1022](http://link.springer.com/article/10.1007%2Fs10955-009-9714-4). [arXiv:0808.2784](http://arxiv.org/abs/0808.2784)
1. J. Schenker, “Eigenvector localization for random band matrices with power law bandwidth,” [Comm. Math. Phys. 290 (2009), 1065-1097](http://link.springer.com/article/10.1007%2Fs00220-009-0798-0). [arXiv:0809.4405](http://arxiv.org/abs/0809.4405)
1. E. Hamza, Y. Kang, J. Schenker, “Diffusive propagation of wave packets in a fluctuating periodic potential,”  [Lett. Math. Phys. 95 (2010), 53-66](http://link.springer.com/article/10.1007%2Fs11005-010-0436-y). [arXiv:1002.0599](http://arxiv.org/abs/1002.0599)
1. J. Schenker, “Estimating complex eigenvalues of non-self-adjoint Schrödinger operators via complex dilations,”[Math. Res. Lett. 18 (2011), 755-765](http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2011/0018/0004/MRL-2011-0018-0004-a013.pdf). [arXiv:1007.3552](http://arxiv.org/abs/1007.3552)
1. J. Schenker, “How large is large? Estimating the critical disorder for the Anderson model,” [Lett. Math. Phys., 105 (2015), 1-9](http://link.springer.com/article/10.1007%2Fs11005-014-0729-7). [arXiv:1305.6987](http://arxiv.org/abs/1305.6987)
1. C. Musselman, J. Schenker, “Diffusive scaling for all moments of the Markov Anderson model,”  [Mark. Proc. Rel. Fields. 21 (2015).](http://math-mprf.org/journal/articles/id1376/) [arXiv:1312.2603](http://arxiv.org/abs/1312.2603)
1. J. Schenker, “Diffusion in the Mean for an Ergodic Schrödinger Equation Perturbed by a Fluctuating Potential,”  [Comm. Math. Phys. 339, 859-901 (2015)](http://link.springer.com/article/10.1007%2Fs00220-015-2432-7). [arXiv:1406.4932](http://arxiv.org/abs/1406.4932)
1. J. Fröhlich, J. Schenker, “Quantum Brownian motion for Lindblad dynamics in the presence of disorder,” [J. Math. Phys. 57, 023305 (2016)](http://scitation.aip.org/content/aip/journal/jmp/57/2/10.1063/1.4942233). [arXiv:1506.01921](http://arxiv.org/abs/1506.01921)
1. J. Clark, J. Schenker, “Spectral analysis of a family of symmetric, scale-invariant diffusions with singular coefficients and associated limit theorems,” [Lat. Am. J. Prob. Stat. 13 (1), 265–289 (2016)](http://alea.math.cnrs.fr/articles/v13/13-11.pdf).  [arXiv:1307.4814](http://arxiv.org/abs/1307.4814).
1. C. G. Adams, J. Schenker, P.S. McGhee, L. J. Gut, J. Brunner, J. R. Miller, “Maximizing information yield from pheromone-baited monitoring traps: estimating plume reach, trapping radius, and absolute density of codling moth (Cydia pomonella) in Michigan apple.” [J. Econ. Ent. (2017)](https://doi.org/10.1093/jee/tow258).
1. M. Aizenman, R. Peled, J. Schenker, M. Shamis, S. Sodin “Matrix regularizing effects of Gaussian perturbations,” [Comm. Cont. Math. (2017)](http://dx.doi.org/10.1142/S0219199717500286). [arXiv:1509.01799](http://arxiv.org/abs/1509.01799).
1. C. G. Adams, J. Schenker, P.S. McGhee, L. J. Gut, J. R. Miller, "Line-Trapping of Codling Moth, Cydia pomonella, (Lepidoptera: Tortricidae): a Novel Approach to Improving the Precision of Capture Numbers in Traps Monitoring Pest Density,” [J. Econ. Ent 110(4):1508-1511 (2017)](https://doi.org/10.1093/jee/tox147).
1. J. Schenker, “Trapping planar Brownian motion in a non circular trap”, [ALEA, Lat. Am. J. Probab. Math. Stat. 15, 213–231 (2018)](https://doi.org/10.30757/ALEA.v15-10). [arxiv:1610.09731](https://arxiv.org/abs/1610.09731). 
1. R. Mavi, J. Schenker, “Localization in the Disordered Holstein model,” [Comm. Math. Phys 364, 719-764 (2018)](https://link.springer.com/article/10.1007%2Fs00220-018-3271-0). [arXiv:1709.06621](https://arxiv.org/abs/1709.06621).
1. R. Peled, J. Schenker, M. Shamis, S. Sodin “On the Wegner N-orbital model,” [Int. Math. Res. Not. 2019 (4), 1030-1058 (2019)](https://urldefense.proofpoint.com/v2/url?u=https-3A__academic.oup.com_imrn_article_2019_4_1030_3957590-3FguestAccessKey-3Dfef364ad-2Ddda7-2D4eea-2D9d64-2D0a8f902d5559&d=DwMFaQ&c=nE__W8dFE-shTxStwXtp0A&r=DsnG4IIDv2sNpaDzwvu_MA&m=dv5WtttcTXeBecFWLUvPy4pagm3nM1AhI8HA6faryNQ&s=EG8lMpt-9GwQLJcefj6PrO7gBoRErseVzax_A0LnMhY&e=). [arxiv.org:1608.02922](http://arxiv.org/abs/1608.02922).
1. R. Mavi, J. Schenker, “Resonant Tunneling In A System With Correlated Pure Point Spectrum,” [J. Math. Phys. 60, 052103 (2019)](https://doi.org/10.1063/1.5075623). [arxiv:1705.03039](https://arxiv.org/abs/1705.03039).
1. P. Hislop, K. Kirkpatrick, S. Olla, J. Schenker, “Transport of a quantum particle in a time-dependent white-noise potential,” [J. Math. Phys. 60, 083303 (2019)](https://doi.org/10.1063/1.5054017). [arxiv:1807.08317](https://arxiv.org/abs/1807.08317).
1. J. Schenker, F. Z. Tilocco, S. Zhang, “Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential,” [Commun. Math. Phys. 377, 1697-1563 (2020)](http://link.springer.com/article/10.1007/s00220-020-03692-6), [arxiv:1901.06598](https://arxiv.org/abs/1901.06598).
1. C. Adams, J. Schenker, P. Weston, L. Gut, J. Miller, “Path Meander of Male Codling Moths (Cydia pomonella) Foraging for Sex Pheromone Plumes: Field Validation of a Novel Method for Quantifying Path Meander of Random Movers Developed Using Computer Simulations,” [Insects 11, 549 (2020)](https://www.mdpi.com/2075-4450/11/9/549).
1. R. Matos, J. Schenker, “Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory,” [Commun. Math. Phys. 382, 1725–1768 (2021)](https://link.springer.com/article/10.1007/s00220-020-03933-8). [arXiv:1906.10800](https://arxiv.org/abs/1906.10800).
1. R. Movassagh, J. Schenker, “Theory of Ergodic Quantum Processes,” [Phys. Rev. X 11, 041001 (2021)](https://link.aps.org/doi/10.1103/PhysRevX.11.041001). [arXiv:2004.14397](https://arxiv.org/abs/2004.14397).
1.  F. Klopp, J. Schenker, “On the spatial extent of localized eigenfunctions for random Schrödinger operators”, [Commun. Math. Phys. 394, 679–710 (2022)](https://link.springer.com/epdf/10.1007/s00220-022-04419-5?sharing_token=OXPa0s554j_WU31vP5nVIfe4RwlQNchNByi7wbcMAY7WIg63qpP3nlsAm8ZFC_tAGlv0Tsya5tf6Iq9sAbztpWBWjrCKzL8XYJwPuOZmLM7rPp_45hpzJFowqEmNVjBbntgszTrXEvmCAfQBuGSMbXP-_CDehE6SbEMAogqS0PQ%3D).  [arXiv:2105.13215](https://arxiv.org/abs/2105.13215), 
1. R. Movassagh, J.  Schenker, “An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states,” [Commun. Math. Phys. 395, 1174-1196 (2022).](https://doi.org/10.1007/s00220-022-04448-0) [arXiv:1909.11769](https://arxiv.org/abs/1909.11769)
1. A. Bols, J. Schenker, J. Shapiro, “Fredholm Homotopies for Strongly-Disordered 2D Insulators,” [Commun. Math. Phys. 397, 1163-1190 (2022)](https://doi.org/10.1007/s00220-022-04511-w). [arXiv:2110.07068](https://arxiv.org/abs/2110.07068)
1. L. Pathirana, J. Schenker, “Law of large numbers and central limit theorem for ergodic quantum processes,” [J. Math. Phys 64, 082201 (2023)](https://doi.org/10.1063/5.0153483). [arXiv:2303.08992](https://arxiv.org/abs/2303.08992)
1. R. Matos, R. Mavi, J. Schenker, “Spectral and Dynamical contrast on highly correlated Anderson-type models”, [Ann. Hen. Poinc. 25, 1445-1483 (2023)](https://doi.org/10.1007/s00023-023-01361-7). [arXiv:2011.00684](https://arxiv.org/abs/2011.00684)
1. G. Cipolloni, R. Peled, J. Schenker, J. Shapiro, “Dynamical Localization for Random Band Matrices up to  $ W << N^{1/4} $”, [Commun. Math. Phys. 405 (2024)](https://doi.org/10.1007/s00220-024-04948-1). [arXiv:2206.00545](https://arxiv.org/abs/2206.05545).