Three-velocity coalescing ballistic annihilation. (English) Zbl 1515.60300

Summary: Three-velocity ballistic annihilation is an interacting system in which stationary, left-, and right-moving particles are placed at random throughout the real line and mutually annihilate upon colliding. We introduce a coalescing variant in which collisions may generate new particles. For a symmetric three-parameter family of such systems, we compute the survival probability of stationary particles at a given initial density. This allows us to describe a phase-transition for stationary particle survival.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[1] Vladimir Belitsky and Pablo A. Ferrari, Ballistic annihilation and deterministic surface growth, Journal of Statistical Physics 80 (1995), no. 3, 517-543. · Zbl 1081.60553
[2] RA Blythe, MR Evans, and Y Kafri, Stochastic ballistic annihilation and coalescence, Physical Review Letters 85 (2000), no. 18, 3750.
[3] Nicolas Broutin and Jean-François Marckert, The combinatorics of the colliding bullets, Random Structures & Algorithms 56 (2020), no. 2, 401-431. · Zbl 1446.60008
[4] Debbie Burdinski, Shrey Gupta, and Matthew Junge, The upper threshold in ballistic annihilation, ALEA 16 (2019), 1077-1087. · Zbl 1488.60227
[5] G. F. Carnevale, Y. Pomeau, and W. R. Young, Statistics of ballistic agglomeration, Physical Review Letters 64 (1990), no. 24, 2913-2916.
[6] Padró, Darío Cruzado, Matthew Junge, and Lily Reeves, Arrivals are universal in coalescing ballistic annihilation, 2209.09271 (2022).
[7] Michel Droz, Pierre-Antoine Rey, Laurent Frachebourg, and Jarosław Piasecki, Ballistic-annihilation kinetics for a multivelocity one-dimensional ideal gas, Physical Review 51 (1995), no. 6, 5541-5548 (eng).
[8] Brittany Dygert, Christoph Kinzel, Matthew Junge, Annie Raymond, Erik Slivken, and Jennifer Zhu, The bullet problem with discrete speeds, Electronic Communications in Probability 24 (2019). · Zbl 1488.60230
[9] Yves Elskens and Harry L. Frisch, Annihilation kinetics in the one-dimensional ideal gas, Phys. Rev. A 31 (1985), 3812-3816.
[10] John Haslegrave, Vladas Sidoravicius, and Laurent Tournier, Three-speed ballistic annihilation: phase transition and universality, Selecta Mathematica 27 (2021), no. 84. · Zbl 1470.60279
[11] John Haslegrave and Laurent Tournier, Combinatorial universality in three-speed ballistic annihilation, In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, vol. 77, Springer International Publishing, 2021, pp. 487-517. · Zbl 1469.60336
[12] Junge, Matthew, Arturo Ortiz San Miguel, Lily Reeves, and Cynthia Rivera Sánchez, Non-universality in clustered ballistic annihilation, 2209.04470 (2022). · Zbl 07721294
[13] Matthew Junge and Hanbaek Lyu, The phase structure of asymmetric ballistic annihilation, The Annals of Applied Probability 32.5 (2022) pp. 3797-3816. · Zbl 1498.60388
[14] PL Krapivsky, S Redner, and F Leyvraz, Ballistic annihilation kinetics: The case of discrete velocity distributions, Physical Review E 51 (1995), no. 5, 3977.
[15] PL Krapivsky and Clément Sire, Ballistic annihilation with continuous isotropic initial velocity distribution, Physical review letters 86 (2001), no. 12, 2494.
[16] Vladas Sidoravicius and Laurent Tournier, Note on a one-dimensional system of annihilating particles, Electron. Commun. Probab. 22 (2017), 9 pp. · Zbl 1386.60327
[17] Balint Toth, Alexei Ermakov, and Wendelin Werner, On some annihilating and coalescing systems, Journal of Statistical Physics 91 (1998), no. 5-6, 845-870. · Zbl 0921.60086
[18] Doug Toussaint and Frank Wilczek, Particle-antiparticle annihilation in diffusive motion, Journal of Chemical Physics 78 (1983), no. 5, 2642-2647 (English (US))
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