mathematics

Maury Bramson

Maury Bramson is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Maury Bramson rather than just read about it. In short: Maury Daniel Bramson (born 1951 in New York City) is an American mathematician, specializing in probability theory and mathematical statistics. Education and career Bramson grew up in the Los Angeles area and graduated with a bachelor's degree in mathematics from the University of California, Berkeley after having also attended the University of California, San Diego and having participated in the University of Cali…

Key takeaways

Maury Bramson belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Maury Bramson to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Maury Bramson from memory before moving on to harder problems.

Reference excerpt

Maury Daniel Bramson (born 1951 in New York City) is an American mathematician, specializing in probability theory and mathematical statistics.

Education and career Bramson grew up in the Los Angeles area and graduated with a bachelor's degree in mathematics from the University of California, Berkeley after having also attended the University of California, San Diego and having participated in the University of California's Education Abroad Program at the University of Göttingen. He graduated with a master's degree in statistics from Stanford University. In 1977 he received his PhD from Cornell University with thesis Maximal Displacement of Branching Brownian Motion under the supervision of Harry Kesten. Bramson was an instructor at the Courant Institute of Mathematical Sciences. He was a member of the mathematical faculties of the University of Wisconsin–Madison and the University of California, Davis before becoming a professor at the University of Minnesota. He was at the Institute for Advanced Study for the academic year 1995–1996. Bramson's research deals with models of interacting particle systems, stochastic networks, and branching processes. The models are motivated by physical and biological science, engineering, and computer science. Bramson was an Invited Speaker at the International Congress of Mathematicians in Berlin in 1998. He was elected a Fellow of the American Mathematical Society in the class of 2015 for "contributions to stochastic processes and their applications." He was elected a member of the National Academy of Sciences in 2017. He is also a Fellow of the Institute of Mathematical Statistics.

Selected publications

Articles Bramson, Maury; Griffeath, David (1979). "Renormalizing the 3-Dimensional Voter Model". The Annals of Probability. 7 (3): 418–432. doi:10.1214/aop/1176995043. Bramson, Maury; Griffeath, David (1980). "Asymptotics for interacting particle systems onZ D". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 53 (2): 183–196. doi:10.1007/BF01013315. S2CID 123164606. Bramson, Maury; Lebowitz, Joel L. (1988). "Asymptotic Behavior of Densities in Diffusion-Dominated Annihilation Reactions". Physical Review Letters. 61 (21): 2397–2400. Bibcode:1988PhRvL..61.2397B. doi:10.1103/PhysRevLett.61.2397. PMID 10039107. Andjel, E. D.; Bramson, M. D.; Liggett, T. M. (1988). "Shocks in the asymmetric exclusion process". Probability Theory and Related Fields. 78 (2): 231–247. doi:10.1007/BF00322020. S2CID 123554962. Bramson, Maury; Durrett, Rick (1988). "A simple proof of the stability criterion of Gray and Griffeath". Probability Theory and Related Fields. 80 (2): 293–298. doi:10.1007/BF00356107. S2CID 15722615. Bramson, Maury; Griffeath, David (1989). "Flux and Fixation in Cyclic Particle Systems". The Annals of Probability. 17 (1): 26–45. doi:10.1214/aop/1176991492. JSTOR 2244194. Bramson, M.; Durrett, R.; Swindle, G. (1989). "Statistical Mechanics of Crabgrass". The Annals of Probability. 17 (2): 444–481. doi:10.1214/aop/1176991410. JSTOR 2244276. Bramson, Maury; Durrett, Rick; Schonmann, Roberto H. (1991). "The Contact Processes in a Random Environment". The Annals of Probability. 19 (3): 960–983. doi:10.1214/aop/1176990331. JSTOR 2244469. Lawler, Gregory F.; Bramson, Maury; Griffeath, David (1992). "Internal Diffusion Limited Aggregation". The Annals of Probability. 20 (4): 2117–2140. doi:10.1214/aop/1176989542. JSTOR 2244742. Bramson, Maury (1994). "Instability of FIFO Queueing Networks". The Annals of Applied Probability. 4 (2): 414–431. doi:10.1214/aoap/1177005066. Bramson, Maury (1994). "Instability of FIFO Queueing Networks with Quick Service Times". The Annals of Applied Probability. 4 (3): 693–718. doi:10.1214/aoap/1177004967.

Books Bramson, Maury (1983). Convergence of solutions of the Kolmogorov equation to travelling waves. Providence, R.I.: American Mathematical Society. ISBN 9780821822852. Bramson, Maury; Durrett, Rick Durrett, eds. (1999). Perplexing problems in probability : festschrift in honor of Harry Kesten. Boston: Birkhäuser. 2012 pbk reprint Bramson, Maury (26 June 2008). Stability of Queueing Networks: École d'Été de Probabilités de Saint-Flour XXXVI-2006. Springer Science & Business Media. ISBN 978-3-540-68895-2.

References

Worked examples

Example 1 — a first encounter with Maury Bramson

Start with the simplest possible case. Write down what Maury Bramson claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Maury Bramson before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Maury Bramson ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Maury Bramson

In research: Maury Bramson appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Maury Bramson in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Maury Bramson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, 20th-century American statisticians, 21st-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Maury Bramson outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Maury Bramson in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Maury Bramson means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Maury Bramson in simple terms?

Maury Daniel Bramson (born 1951 in New York City) is an American mathematician, specializing in probability theory and mathematical statistics. Education and career Bramson grew up in the Los Angeles area and graduated with a bachelor's degree in mathematics from the University of California, Berke…

Why does Maury Bramson matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Maury Bramson?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Maury Bramson.