Daniel Kious

Research Interests

I work in the pure end of probability theory, my expertise lies in the study of  random walks with self-interaction, random walks in random environments, random walks in dynamic random environments, processes with reinforcement, branching processes.

Publications

20- Sharp threshold for the ballisticity of the random walk on the exclusion process, 2024, with G. Conchon--Kerjan and P.-F. Rodriguez, preprint.

19- Aging and sub-aging for one-dimensional random walks amongst random conductances, with D. Croydon and C. Scali

18- Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh, with R. Baldasso, M. Hilário and A. Teixeira, 2023, preprint.

17- Scaling limit of critical random trees in random environment, 2022, with G. Conchon--Kerjan and C. Mailler, Electronic Journal of Probability (to appear).

16- Coexistence of lazy frogs on Z, with Mark Holmes, 2021, Journal of Applied Probability (to appear)

15- The trace-reinforced ants process does not find shortest paths 2021, with C. Mailler and B. Schapira, Journal de l'Ecole Polytechnique (to appear).

14- Finding geodesics on graphs using reinforcement learning, 2020, with C. Mailler and B. Schapira, Annals of Applied Probability (to appear).

13- Random Memory Walk, with A. Fribergh, V. Sidoravicius and A. Stauffer, 2020, In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, 439-453.

12- Random walk on the simple symmetric exclusion process, with M. Hilário and A. Teixeira, 2020,  Communications in Mathematical Physics, 379, 61-101. 

11-A Monotonicity Property for Once Reinforced Biased Random Walk on Z^d, with Mark Holmes, 2019, Sojourns in Probability Theory and Statistical Physics - III, pp 255-273, Springer

10- The branching-ruin number as critical parameter of random processes on trees, with A. Collevecchio and C.-B. Huynh, 2018, Electronic Journal of Probability (to appear).

9- Once reinforced random walk on ZxΓ, with B. Schapira and A. Singh, 2021, Ann. Inst. H. Poincare Probab. Statist. 57 (4), 2219--2242.

8- Explicit formula for the density of local times of Markov Jump Processes, with R. Huang, P. Tarrès and V. Sidoravicius, 2018, Electronic Communications in Probability, 23 (90).

7- The branching-ruin number and the critical parameter of once-reinforced random walk on trees, with A. Collevecchio and V. Sidoravicius, 2019,  Communications on Pure and Applied Mathematics (to appear).

6- On the speed of once-reinforced biased random walk on trees, with Andrea Collevecchio and Mark Holmes, 2018, Electronic Journal of Probability, 23 (86).

5- Phase transition for the Once-reinforced random walk on Z^d-like trees, with Vladas Sidoravicius, 2018, The Annals of Probability, 46 (4), 2121--2133.

4- Scaling limits for sub-ballistic biased random walks in random conductances, with Alex Fribergh, 2018, The Annals of Probability, 46 (2), 605--686. 

3- Reinforcement learning in social networks, with Pierre Tarrès, 2015, preprint. 

2- Local trapping for elliptic random walks in random environments in Z^d, with Alex Fribergh, 2014, Probability Theory and Related Fields, 165(3), 795--834, or on arXiv. 

1- Stuck Walks: a conjecture of Erschler, Tóth and Werner, 2016, The Annals of Probability, 44(2), 883--923.

0- PhD Thesis: I defended my PhD in June 2014 at the IMT, Université Paul Sabatier, Toulouse, under the supervision of Pierre Tarrès. Here is the manuscript.

TCC Course: (Atypical) behaviour of random walks in random and dynamical environment

From October 2024 to December 2024, I will be giving an online Taught Course Centre (TCC) course on trapping phenomena for random walks in random environment.

I will be posting my lectures notes HERE.

Events

Upcoming Conference!!

• Random Walks, Percolation and Mixing Time, 9-13 June 2025, ICMS, Edinburgh.

• CUWB IV: Frontiers in statistics and probability, Mexico City, 7-11 April 2025.

Past conference:

• CUWB2: Probability-on-sea in Playa del Carmen, Mexico, 8-12 January 2023. Website.

• Conference Random Walks in Bath, 5-9 June 2023. Info at https://sites.google.com/view/rw-in-bath/.

• Conference BUC in Guanajuato, 16-20 January 2023: Website.

Postdoc

-Guillaume Conchon-Kerjan, July 2021 - April 2023, EPSRC-Funded, now Lecturer at King's College London.
-Umberto De Ambroggio, March-September 2022, co-supervised by Matt Roberts, now postdoc at LMU München.

PhD Students

-Wilfred Armfield, do-supervised by Cécile Mailler, started Sept. 2022, SAMBa student.
-Pawel Rudnicki, defended June 2024, URSA funded, SAMBa-aligned.
-Carlo Scali, defended July 2023, SAMBa student.

Miscellaneous

• I have written in 2016 a short article for the CIJM, a french committee for the popularization of Mathematics, on the theme of "Social networks".

• I train, and compete in, Brazilian Jiu Jitsu. I am a blue belt under Professor Callum Swift at Gracie Barra Frome.