I am an assistant professor in the Department of Mathematics at the University of Hawaiʻi at Mānoa. Before joining UH Mānoa, I was an Alexander von Humboldt postdoc fellow and a Technical University Foundation Fellow at the Technical University Munich, Germany, hosted by Professor Christian Kuehn. During 2018.7-2020.6, I was a postdoctoral fellow advised by Professor Carsten Wiuf at the University of Copenhagen, Denmark. In 05/2018, I graduated as a PhD in Applied Math at the University of Alberta, Canada, under the supervision of Professor Arno Berger.

2017, Vancouver. Photo credit: Dr. Hui Wang.

Teaching

Fall 2026: Linear Algebra and Differential Equations (MATH 307)

Stochastic Dynamical Networks (MATH 649(K))

Past Teaching

Spring 2026: Introduction to Linear Algebra (MATH 311)

Calculus III (MATH 243)

Fall 2025: Probability (MATH 471)

Spring 2025: Accelerated Calculus III (MATH 253A)

Linear Algebra and Differential Equations (MATH 307)

Fall 2024: Probability (MATH 471)

Fall 2023: Theory of Functions of a Real Variable (MATH 631)

Linear Algebra and Differential Equations (MATH 307)

Spring 2023: Applied Calculus II (MATH 216)

Fall 2022: Introduction to Differential Equations (MATH 302)

Research Interests

Broadly speaking, I work in applied probability and applied dynamical systems. Specifically, I am interested in chemical reaction network theory (CRNT) and limit theory of large dynamical networks, as well as the tools from approximation theory for studying limits of large dynamical networks. Research questions generally stem from systems biology and network science. My research is currently funded by the Simons Foundation (Travel Support for Mathematicians: MP-TSM-00002379).

Journal Articles (CRNT&Math Biology, Limits of Large Networks&PDE,Approximation Theory)

Howells, A. S., Cappelletti, D., and Xu, C. (2025): Stability of randomly switching stochastic reaction networks with asymptotically linear transition rates, Preprint, arXiv:2507.09421. 36 pp.
Xu, C. (2026): Exponential ergodicity of first order endotactic stochastic reaction systems. arXiv:2601.00176. 19 pp.
Xu, C. (2026): On the regularity of reaction systems. To appear. SIAM Journal on Applied Mathematics. A preprint version: arXiv:2409.05340, 21pp.
Xu, C. (2026): First-order endotactic reaction networks. Journal of Mathematical Biology. 92(74), doi.org/10.1007/s00285-026-02378-2. A preprint version: arXiv:2409.01598.
Hansen, M.C., Wiuf, C. and Xu, C. (2025): Stationary measures of continuous time Markov chains with applications to stochastic reaction networks. Advances in Applied Probability, 57(3): 1031-1067. A preprint version: arXiv:2312.06186.
Kuehn, C. and Xu, C. (2025): Vlasov equation on directed hypergraph measures. Partial Differential Equations and Applications, 6(9), doi.org/10.1007/s42985-025-00313-6. A preprint version: arXiv:2207.03806.
Gkogkas, M.A., Kuehn, C., and Xu, C. (2025): Mean field limits of co-evolutionary signed heterogeneous networks. European Journal of Applied Mathematics, 37(3), 643-686. A preprint version: arXiv:2207.03806.
Xu, C., Hansen, M.C., and Wiuf, C. (2024): The asymptotic tails of limit distributions of continuous time Markov chains, Advances in Applied Probability, 56(2): 693-734. A preprint version: arXiv:2007.11390.
Xu, C., Hansen, M.C., and Wiuf, C. (2023): Full classification of dynamics for one-dimensional continuous time Markov chains with polynomial transition rates, Advances in Applied Probability, 55(1): 321-355. A preprint version: arXiv:2006.10548.
Gkogkas, M.A., Kuehn, C., and Xu, C. (2023): Continuum limits for adaptive network dynamics, Communications in Mathematical Sciences, 21(1), 83-106. A preprint version: arXiv:2109.05898.
Kuehn, C. and Xu, C. (2022): Vlasov equations on digraph measures, Journal of Differential Equations, 339(5), 261-349. A preprint version: arXiv:2107.08419.
Xu, C., Hansen, M.C., and Wiuf, C. (2022): Structural classification of continuous time Markov chains with applications, Stochastics, 94(7), 1003-1030. A preprint version: arXiv:2006.09802.
Berger, A. and Xu, C. (2020): Asymptotics of one-dimensional Lévy approximations. Journal of Theoretical Probability, 33, 1164-1195. A preprint version: arXiv:1809.07891.
Xu, C. and Berger, A. (2019): Best finite constrained approximations of one-dimensional probabilities. Journal of Approximation Theory, 244, 1-36. A preprint version: arXiv:1704.07871.
Berger, A. and Xu, C. (2019): Best finite approximations of Benford’s law. Journal of Theoretical Probability, 32, 1525-1553. A preprint version: arXiv:1803.10370.
Xu, C. (2019): The distributional asymptotics mod 1 of $(log_b n)$. Uniform Distribution Theory, 14(1), 105-122. A preprint version: arXiv:1609.08207.
Xu, C. (2017): Circularly uniformizable invariant probability measures for linear transformations. Journal of Mathematical Analysis and Applications, 455(1), 778-791. A preprint version: arXiv:1609.08204.
Xu, C. (2017): Threshold dynamics of a stochastic Keizer’s model with stochastic incidence. Journal of Mathematical Chemistry, 55, 1034-1045.
Xu, C. (2017): Global threshold dynamics of a stochastic differential equation SIS model. Journal of Mathematical Analysis and Applications, 447(2), 736-757. A preprint version: arXiv:1506.02342.
Xu, C. (2016): Strong Allee effect in a stochastic logistic model with mate limitation and stochastic immigration, Discrete and Continuous Dynamical System-B, 21(7), 2321-2336. A preprint version: arXiv:1605.06084.
Xu, C. (2015): On the idempotency, involution and nilpotency of a linear combination of two matrices, Linear and Multilinear Algebra, 63(8), 1664-1677.
Xu, R. and Xu, C. (2013): Sharp conditions of global existence for second-order derivative nonlinear Schrödinger equations with combined power-type nonlinearities, Zeitschrift für Angewandte Mathematik und Mechanik, 93(1), 29-37.
Xu, C. and Wei, J. (2012): On stability of two degenerate reaction-diffusion systems, Journal of Mathematical Analysis and Applications, 390(1), 126-135.
Xu, C. and Wei, J. (2012): Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model, Nonlinear Analysis: Real World Applications, 13(4), 1961-1977.
Xu, R. and Xu, C. (2012): Cross-constrained problems for nonlinear Schrödinger equation with harmonic potential, Electronic Journal of Differential Equations, 2012(211), 1-12.
Xu, C. and Xu, R. (2012): Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute, Linear Algebra and its Applications, 437(9), 2091-2109.

Book Chapters

Wiuf, C. and Xu, C. (2021): Fiber decomposition of deterministic reaction networks with applications. Paper No. 22, in “Contemporary Research in Mathematical Biology: Modeling, Computation and Analysis”, ed. by Cantrell et al., Contemporary Mathematics and Its Applications: Monographs, Expositions and Lecture Notes, World Scientific, to appear in May 2027. A preprint version: arXiv:2107.09706. 14 pp.

Unpublished Manuscripts

Wiuf, C. and Xu, C. (2023): Stationary measures of continuous time Markov chains with applications to stochastic reaction networks, Preprint, arXiv:2312.07590. pp.3
Wiuf, C. and Xu, C. (2020): Classification and threshold dynamics of stochastic reaction networks, arXiv:2012.07954. pp. 17.

Recorded Talks on CRNT

An old talk: "Dynamics of One-Dimensional Stochastic Reaction Networks"

A recent talk: "Regularity of Chemical Reaction Networks"

A regular online seminar on CRNT:

Seminar on the Mathematics of Reaction Networks

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